537 results
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2. A note on a paper by D.K.R. Babajee and M.Z. Dauhoo
- Author
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Ren, Hongmin
- Subjects
- *
STOCHASTIC convergence , *MATHEMATICAL optimization , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
3. The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function.
- Author
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Trojovský, Pavel and Venkatachalam, K.
- Subjects
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ITERATIVE methods (Mathematics) , *LOGICAL prediction , *COEFFICIENTS (Statistics) , *BINOMIAL coefficients , *MATHEMATICAL analysis - Abstract
In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function hl(z) = z2 +l. Their generalization was based on the composition of hl with the Möbius transformation m(z) = 1z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of m(hl(z)) (at z = 0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
4. Regularity for the weak solutions to certain parabolic systems under certain growth condition.
- Author
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Jia, Cuiman and Tan, Zhong
- Subjects
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LAPLACIAN matrices , *MATHEMATICAL bounds , *NONLINEAR systems , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract In this paper, we consider the regularity of the weak solutions to a quasilinear parabolic systems which is a generalization of p -Laplacian of the type u t i − (A α i (∇ u)) x α = f i (x , t , u , ∇ u) , i = 1 , … , N where the main part satisfies some ellipticity and f i satisfies certain growth conditions. We prove boundedness of the solutions and the gradients of solutions to the systems by the means of the energy estimates and a nonlinear iteration procedure of the Moser type in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
5. Weak and Strong Convergence Theorems for the Multiple-Set Split Equality Common Fixed-Point Problems of Demicontractive Mappings.
- Author
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Wang, Yaqin, Kim, Tae-Hwa, and Fang, Xiaoli
- Subjects
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MATHEMATICAL analysis , *MATHEMATICS theorems , *ALGORITHMS , *EQUALITY , *ITERATIVE methods (Mathematics) - Abstract
We consider mixed parallel and cyclic iterative algorithms in this paper to solve the multiple-set split equality common fixed-point problem which is a generalization of the split equality problem and the split feasibility problem for the demicontractive mappings without prior knowledge of operator norms in real Hilbert spaces. Some weak and strong convergence results are established. The results obtained in this paper generalize and improve the recent ones announced by many others. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
6. Efficient hybrid group iterative methods in the solution of two-dimensional time fractional cable equation.
- Author
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Salama, Fouad Mohammad, Hj. Mohd. Ali, Norhashidah, and Abd Hamid, Nur Nadiah
- Subjects
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PARTIAL differential equations , *LAPLACE transformation , *FINITE differences , *EQUATIONS , *MATHEMATICAL analysis , *MATRIX norms , *ITERATIVE methods (Mathematics) - Abstract
In this paper, the development of new hybrid group iterative methods for the numerical solution of a two-dimensional time-fractional cable equation is presented. We use Laplace transform method to approximate the time fractional derivative which reduces the problem into an approximating partial differential equation. The obtained partial differential equation is solved by four-point group iterative methods derived from two implicit finite difference schemes. Matrix norm analysis together with mathematical induction are utilized to investigate the stability and convergence properties. A comparative study with the recently developed hybrid standard point (HSP) iterative method accompanied by their computational cost analysis are also given. Numerical experiments are conducted to demonstrate the superiority of the proposed hybrid group iterative methods over the HSP iterative method in terms of the number of iterations, computational cost as well as the CPU times. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
7. A NOTE ON BOUNDED SOLUTIONS OF AN ITERATIVE EQUATION.
- Author
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HOU YU ZHAO and JIA LIU
- Subjects
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ITERATIVE methods (Mathematics) , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *FIXED point theory , *FUNCTIONAL analysis , *EQUATIONS , *MATHEMATICS - Abstract
In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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8. A Geometric Analysis of Phase Retrieval.
- Author
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Sun, Ju, Qu, Qing, and Wright, John
- Subjects
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GEOMETRIC analysis , *BIVECTORS , *PROBABILITY theory , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of m measurements, yk=ak∗x
for k=1,…,m , is it possible to recover x∈Cn (i.e., length-n complex vector)? This generalized phase retrieval (GPR) problem is a fundamental task in various disciplines and has been the subject of much recent investigation. Natural nonconvex heuristics often work remarkably well for GPR in practice, but lack clear theoretic explanations. In this paper, we take a step toward bridging this gap. We prove that when the measurement vectors ak ’s are generic (i.i.d. complex Gaussian) and numerous enough (m≥Cnlog3n ), with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) There are no spurious local minimizers, and all global minimizers are equal to the target signal x , up to a global phase, and (2) the objective function has a negative directional curvature around each saddle point. This structure allows a number of iterative optimization methods to efficiently find a global minimizer, without special initialization. To corroborate the claim, we describe and analyze a second-order trust-region algorithm. [ABSTRACT FROM AUTHOR] - Published
- 2018
- Full Text
- View/download PDF
9. On the Bessel operator ...Bt related to the Bessel-Helmholtz and Bessel Klein-Gordon operator.
- Author
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Bupasiri, Sudprathai
- Subjects
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HELMHOLTZ equation , *KLEIN-Gordon equation , *DIMENSIONS , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
In this paper, we study the Bessel operator ...Bt, iterated t-times and denote by ...Bt = ((Ba1 + . . . + Bap + m²)² - Bap+1 + . . . + Bap+q)²)² where p + q = n, Bai= ... + 2vi/ai .../...ai, 2vi = 2αi + 1; αi > -1/2, ai > 0, t ∈ ℤ+ ∪ {0}, m ∈ ℝ+ ∪ {0} and p + q = n is the dimension of ℝn+ = {a : a = (a1, . . ., an), a1 > 0, . . ., an > 0}. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
10. The ball-relaxed CQ algorithms for the split feasibility problem.
- Author
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Yu, Hai, Zhan, Wanrong, and Wang, Fenghui
- Subjects
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ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *NUMERICAL analysis , *LAGRANGE equations , *APPROXIMATION theory - Abstract
The split feasibility problem (SFP) is to find so that , where C and Q are non-empty closed convex subsets in Hilbert spaces and , respectively, and A is a linear bounded operator from to . Byrne proposed an iterative method called the CQ algorithm that involves the orthogonal projections onto C and Q. However, the projections onto C and Q might be hard to be implemented in general. In this paper, we propose a ball-relaxed projection method for the SFP. Instead of half spaces, we replace C and Q in the proposed algorithm by two properly chosen closed balls and . Since the projection onto the closed ball has closed form, the proposed algorithm is thus easy to be implemented. Under some mild conditions, we establish the weak convergence of the proposed algorithm to a solution of the SFP. As an application, we obtain new algorithms for solving the split equality problem. Preliminary numerical experiments show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
11. Iterative methods for finding commuting solutions of the Yang–Baxter-like matrix equation.
- Author
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Kumar, Ashim and Cardoso, João R.
- Subjects
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YANG-Baxter equation , *ITERATIVE methods (Mathematics) , *NUMERICAL solutions to equations , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
The main goal of this paper is the numerical computation of solutions of the so-called Yang–Baxter-like matrix equation A X A = X A X , where A is a given complex square matrix. Two novel matrix iterations are proposed, both having second-order convergence. A sign modification in one of the iterations gives rise to a third matrix iteration. Strategies for finding starting approximations are discussed as well as a technique for estimating the relative error. One of the methods involves a very small cost per iteration and is shown to be stable. Numerical experiments are carried out to illustrate the effectiveness of the new methods. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
12. POSITIVITY OF ITERATED SEQUENCES OF POLYNOMIALS.
- Author
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BAO-XUAN ZHU
- Subjects
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ITERATIVE methods (Mathematics) , *POLYNOMIALS , *GEOMETRIC series , *MATHEMATICAL analysis , *GEOMETRIC dissections - Abstract
In this paper, we present some criteria for the 2-q-log-convexity and 3-q-log-convexity of combinatorial sequences, which can be regarded as the first column of a certain infinite triangular array [An,k(q)]n,k≥0 of polynomials in q with nonnegative coefficients satisfying the recurrence relation An,k(q) = An-1,k-1(q) + gk(q)An-1,k(q) + hk+1(q)An-1,k+1(q): Those criteria can also be presented by continued fractions and generating functions. These allow a unified treatment of the 2-q-log-convexity of alternating Eulerian polynomials, 2-log-convexity of Euler numbers, and 3-q-logconvexity of many classical polynomials, including the Bell polynomials, the Eulerian polynomials of types A and B, the q-Schröder numbers, q-central Delannoy numbers, the Narayana polynomials of types A and B, the generating functions of rows in the Catalan triangles of Aigner and Shapiro, the generating functions of rows in the large Schröder triangle, and so on, which extend many known results for q-log-convexity. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
13. A modified interval symmetric single step procedure ISS-5D for simultaneous inclusion of polynomial zeros.
- Author
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Sham, Atiyah W. M., Monsi, Mansor, Hassan, Nasruddin, and Suleiman, Mohamed
- Subjects
- *
INTERVAL analysis , *MATHEMATICAL symmetry , *POLYNOMIALS , *ZERO (The number) , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
The aim of this paper is to present a new modified interval symmetric single-step procedure ISS-5D which is the extension from the previous procedure, ISS1. The ISS-5D method will produce successively smaller intervals that are guaranteed to still contain the zeros. The efficiency of this method is measured on the CPU times and the number of iteration. The procedure is run on five test polynomials and the results obtained are shown in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
14. The omega-rule interpretation of transfinite provability logic.
- Author
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Fernández-Duque, David and Joosten, Joost J.
- Subjects
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LOGIC , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *PROBABILITY theory , *MATHEMATICS - Abstract
Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
15. Mathematical analysis of schema survival for genetic algorithms having dual mutation.
- Author
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Mishra, Apoorva and Shukla, Anupam
- Subjects
- *
MATHEMATICAL analysis , *GENETIC algorithms , *COMBINATORIAL optimization , *ITERATIVE methods (Mathematics) , *FUZZY decision making - Abstract
Genetic algorithms are widely used in the field of optimization. Schema theory forms the foundational basis for the success of genetic algorithms. Traditional genetic algorithms involve only a single mutation phase per iteration of the algorithm. In this paper, a novel concept of genetic algorithms involving two mutation steps per iteration is proposed. The purpose of adding a second mutation phase is to improve the explorative power of the genetic algorithms. All the possible cases regarding the working of the proposed variant of the genetic algorithms are explored. After a meticulous analysis of all these cases, three lemmas are proposed regarding the survival of a schema after the application of the dual mutation. Based on these three lemmas, a theorem is proved, and a mathematical expression representing the probability of survival of a schema after the application of the crossover and dual mutation is derived. This expression provides a new insight about the penetration of a schema for such scenario and improves our understanding of the functioning of this modified form of the genetic algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
16. Complex-extrapolated MHSS iteration method for singular complex symmetric linear systems.
- Author
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Zeng, Min-Li and Zhang, Guo-Feng
- Subjects
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LINEAR systems , *ITERATIVE methods (Mathematics) , *STOCHASTIC convergence , *LINEAR differential equations , *MATHEMATICAL analysis - Abstract
In this paper, by extrapolating the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method with a complex relaxation parameter, a complex-extrapolated MHSS (CMHSS) iteration method is present for solving a class of complex singular symmetric of linear equations. We study the semi-convergence properties of the CMHSS iteration method and the extent of the optimal iterative parameters. Furthermore, the convergence conditions also hold for solving nonsingular complex systems. Numerical experiments are given to verify the effectiveness of the CMHSS iteration method for solving both singular and nonsingular complex symmetric systems. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
17. Hyers–Ulam stability of the iterative equation with a general boundary restriction.
- Author
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Xia, Chao
- Subjects
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ITERATIVE methods (Mathematics) , *BOUNDARY value problems , *FUNCTIONAL equations , *LINEAR operators , *MATHEMATICAL analysis - Abstract
Hyers–Ulam stability has played an important role not only in the theory of functional equations but also in a variety of branches of mathematics, such as differential equations, integral equations and linear operators. In the present paper we will discuss the Hyers–Ulam stability of the iterative equation with a general boundary restriction. By the construction of a uniformly convergent sequence of functions, we prove that for every approximate solution of such an equation, there exists an exact solution near it. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
18. Ledrappier–Young formula and exact dimensionality of self-affine measures.
- Author
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Bárány, Balázs and Käenmäki, Antti
- Subjects
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PLANE geometry , *MATHEMATICAL functions , *ITERATIVE methods (Mathematics) , *MATHEMATICAL formulas , *MATHEMATICAL analysis - Abstract
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier–Young formula. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
19. Modulus-based iterative methods for constrained Tikhonov regularization.
- Author
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Bai, Zhong-Zhi, Buccini, Alessandro, Hayami, Ken, Reichel, Lothar, Yin, Jun-Feng, and Zheng, Ning
- Subjects
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ITERATIVE methods (Mathematics) , *TIKHONOV regularization , *KRYLOV subspace , *IMAGE reconstruction , *MATHEMATICAL analysis - Abstract
Tikhonov regularization is one of the most popular methods for the solution of linear discrete ill-posed problems. In many applications the desired solution is known to lie in the nonnegative cone. It is then natural to require that the approximate solution determined by Tikhonov regularization also lies in this cone. The present paper describes two iterative methods, that employ modulus-based iterative methods, to compute approximate solutions in the nonnegative cone of large-scale Tikhonov regularization problems. The first method considered consists of two steps: first the given linear discrete ill-posed problem is reduced to a small problem by a Krylov subspace method, and then the reduced Tikhonov regularization problems so obtained is solved. The second method described explores the structure of certain image restoration problems. Computed examples illustrate the performances of these methods. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
20. Two-fold Mellin–Barnes transforms of Usyukina–Davydychev functions.
- Author
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Kniehl, Bernd A., Kondrashuk, Igor, Notte-Cuello, Eduardo A., Parra-Ferrada, Ivan, and Rojas-Medar, Marko
- Subjects
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H-functions , *POLYNOMIALS , *LOGARITHMS , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *COEFFICIENTS (Statistics) - Abstract
Abstract: In our previous paper (Allendes et al., 2013 [10]), we showed that multi-fold Mellin–Barnes (MB) transforms of Usyukina–Davydychev (UD) functions may be reduced to two-fold MB transforms. The MB transforms were written there as polynomials of logarithms of ratios of squares of the external momenta with certain coefficients. We also showed that these coefficients have a combinatoric origin. In this paper, we present an explicit formula for these coefficients. The procedure of recovering the coefficients is based on taking the double-uniform limit in certain series of smooth functions of two variables which is constructed according to a pre-determined iterative way. The result is obtained by using basic methods of mathematical analysis. We observe that the finiteness of the limit of this iterative chain of smooth functions should reflect itself in other mathematical constructions, too, since it is not related in any way to the explicit form of the MB transforms. This finite double-uniform limit is represented in terms of a differential operator with respect to an auxiliary parameter which acts on the integrand of a certain two-fold MB integral. To demonstrate that our result is compatible with original representations of UD functions, we reproduce the integrands of these original integral representations by applying this differential operator to the integrand of the simple integral representation of the scalar triangle four-dimensional integral . [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
21. Iterated twisted tensor products of nonlocal vertex algebras
- Author
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Sun, Jiancai
- Subjects
- *
ITERATIVE methods (Mathematics) , *VERTEX operator algebras , *MATHEMATICAL analysis , *MATHEMATICAL proofs , *FACTOR analysis , *TENSOR products - Abstract
Abstract: This is the second paper in a series devoted to studies of twisted tensor products of nonlocal vertex algebras. In this paper we introduce and study iterated twisted tensor products of nonlocal vertex algebras. Among the main results, we find conditions for constructing an iterated twisted tensor product of three factors, and prove that those conditions are enough for building an iterated twisted tensor product of any number of factors. And we also establish a universal property and give a characterization of an iterated twisted tensor product. Furthermore, we give an example of iterated twisted tensor product nonlocal vertex algebra. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
22. Simulation-based confidence bounds for two-stage stochastic programs.
- Author
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Glynn, Peter and Infanger, Gerd
- Subjects
- *
ACADEMIC rigor (Education) , *STOCHASTIC analysis , *ITERATIVE methods (Mathematics) , *MATHEMATICAL bounds , *MATHEMATICAL analysis , *STOCHASTIC processes - Abstract
This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (A probabilistic lower bound for two-stage stochastic programs, Stanford University, CA, ) for an iterative sampling-based decomposition algorithm, introduced by Dantzig and Glynn (Ann. Oper. Res. 22:1-21, ) and Infanger (Ann. Oper. Res. 39:41-67, ), for solving two-stage stochastic programs. The paper provides confidence bounds in the presence of both independent sampling across iterations, and when common samples are used across different iterations. Confidence bounds for sample-average approximation then follow as a special case. Extensions of the theory to cover use of variance reduction and the dropping of cuts are also presented. An extensive empirical investigation of the performance of these bounds establishes that the bounds perform reasonably on realistic problems. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
23. A family of iterative methods for computing Moore–Penrose inverse of a matrix
- Author
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Weiguo, Li, Juan, Li, and Tiantian, Qiao
- Subjects
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ITERATIVE methods (Mathematics) , *MATRIX inversion , *APPROXIMATION theory , *MATHEMATICAL sequences , *STOCHASTIC convergence , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: This paper improves on generalized properties of a family of iterative methods to compute the approximate inverses of square matrices originally proposed in [1]. And while the methods of [1] can be used to compute the inner inverses of any matrix, it has not been proved that these sequences converge (in norm) to a fixed inner inverse of the matrix. In this paper, it is proved that the sequences indeed are convergent to a fixed inner inverse of the matrix which is the Moore–Penrose inverse of the matrix. The convergence proof of these sequences is given by fundamental matrix calculus, and numerical experiments show that the third-order iterations are as good as the second-order iterations. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
24. Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings.
- Author
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De la Sen, M.
- Subjects
- *
MATHEMATICAL mappings , *FIXED point theory , *UNIQUENESS (Mathematics) , *ITERATIVE methods (Mathematics) , *MATHEMATICAL sequences , *BANACH spaces , *MATHEMATICAL analysis - Abstract
This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and socalled, contractive precyclic self-mappings which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
25. MÖBIUS ITERATED FUNCTION SYSTEMS.
- Author
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VINCE, ANDREW
- Subjects
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ITERATIVE methods (Mathematics) , *MATHEMATICAL functions , *MOBIUS transformations , *PROJECTIVE spaces , *TOPOLOGY , *ATTRACTORS (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICAL complex analysis - Abstract
Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, in terms of topological, geometric, and dynamical properties, of Möbius iterated function systems that possess an attractor. The paper also includes results on the duality between the attractor and repeller of a Möbius iterated function system. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
26. Stability of King’s family of iterative methods with memory.
- Author
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Campos, Beatriz, Cordero, Alicia, Torregrosa, Juan R., and Vindel, Pura
- Subjects
- *
ITERATIVE methods (Mathematics) , *NONLINEAR equations , *FIXED point theory , *STABILITY theory , *MATHEMATICAL analysis - Abstract
In the literature exist many iterative methods with memory for solving nonlinear equations, the most of them designed in the last years. As they use the information of (at least) the two previous iterates to generate the new one, usual techniques of complex dynamics are not useful in this case. In this paper, we present some real multidimensional dynamical tools to undertake this task, applied on a very well-known family of iterative schemes; King’s class. It is showed that the most of elements of this class present a very stable behavior, visualized in different dynamical planes. However, pathological cases as attracting strange fixed points or periodic orbits can also be found. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
27. A non-iterative immersed boundary method for spherical particles of arbitrary density ratio.
- Author
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Tschisgale, Silvio, Kempe, Tobias, and Fröhlich, Jochen
- Subjects
- *
BOUNDARY value problems , *ITERATIVE methods (Mathematics) , *PARTICLE size determination , *SOLID-liquid equilibrium , *MATHEMATICAL analysis - Abstract
In this paper an immersed boundary method with semi-implicit fluid–solid coupling for mobile particles of arbitrary density ratio is developed. The new scheme does not require any iterations to balance fluid forces and particle forces at the interface. A new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a Lagrangian layer surrounding the particle surface. Furthermore, it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution. On this basis a new time integration scheme is obtained which is unconditionally stable for all fluid–solid density ratios and enables large time steps, with Courant numbers around unity. The new scheme is extensively validated for various test cases and its convergence is assessed. An appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps, making it easy to implement in present codes with explicit coupling. This substantially extends the field of application of such methods. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
28. New results for the Hankel transform via the Hankel potential and Hankel resolvent.
- Author
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Mejjaoli, Hatem
- Subjects
- *
HANKEL functions , *RESOLVENTS (Mathematics) , *ITERATIVE methods (Mathematics) , *POTENTIAL theory (Mathematics) , *MATHEMATICAL analysis - Abstract
In this paper, we characterize the support of the Hankel transform under the behaviour of-norms of iterated Hankel resolvent. Next, we extend the result under the behaviour of-norms of iterated Hankel potentials. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
29. Duality relation on spectra of self-affine measures.
- Author
-
Li, Jian‐Lin
- Subjects
- *
DUALITY theory (Mathematics) , *ALGEBRAIC geometry , *ITERATIVE methods (Mathematics) , *MATHEMATICAL functions , *MATHEMATICAL analysis - Abstract
The present paper establishes a duality relation for the spectra of self-affine measures. This is done under the condition of compatible pair and is motivated by a duality conjecture of Dutkay and Jorgensen on the spectrality of self-affine measures. For the spectral self-affine measure, we first obtain a structural property of spectra which indicates that one can get new spectra from old ones. We then establish a duality property for the spectra which confirms the conjecture in a certain case. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
30. A Predictor-corrector Infeasible-interior-point Algorithm for Semidefinite Optimization in a Wide Neighborhood.
- Author
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Kheirfam, Behrouz
- Subjects
- *
INTERIOR-point methods , *SEMIDEFINITE programming , *MATHEMATICAL optimization , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
In this paper, we propose a predictor-corrector infeasible interior-point algorithm for semidefinite optimization based on the Nesterov-Todd scaling scheme. In each iteration, the algorithm computes the new iterate using a new combination of the predictor and corrector directions. Using the Ai-Zhang's wide neighborhood for linear complementarity problems, and extended to semidefinite optimization by Li and Terlaky, it is shown that the iteration complexity bound of the algorithm is ..., where n is the dimension of the problem and ɛ is the required precision. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
31. An improved active shape model method for facial landmarking based on relative position feature.
- Author
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Chen, Hengxin, Gao, Mingqi, and Fang, Bin
- Subjects
- *
FACE perception , *ITERATIVE methods (Mathematics) , *ERROR analysis in mathematics , *MATHEMATICAL analysis , *DISPLACEMENT (Mechanics) - Abstract
Active Shape Model (ASM) is a most effective method of facial landmarking. It employs two models, profile model and shape model, to match the position of facial landmark. In this paper, we introduce a new model based on relative position feature (RPF) in local region to improve ASM. We found the fact that landmarks with larger matching error have more shape matching displacement. So, in our method, RPF model is used to adjust the position of landmarks with more shape matching displacement in every matching iteration. STASM (Stacked ASM) is practical standard of ASM and is proved to be the best method of locating face landmarks. Our experiments on STASM show significant performance improving, especially on databases in which faces are partially blocked by glasses or artificial black square. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
32. Explicit iteration to Hadamard fractional integro-differential equations on infinite domain.
- Author
-
Wang, Guotao, Pei, Ke, and Baleanu, Dumitru
- Subjects
- *
ITERATIVE methods (Mathematics) , *INTEGRO-differential equations , *BOUNDARY value problems , *INFINITY (Mathematics) , *MATHEMATICAL analysis - Abstract
This paper investigates the existence of the unique solution for a Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equation with the monotone iterative technique. Two examples to illustrate our result are given. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
33. Iterative methods of strong convergence theorems for the split feasibility problem in Hilbert spaces.
- Author
-
Tang, Yuchao and Liu, Liwei
- Subjects
- *
HILBERT space , *ITERATIVE methods (Mathematics) , *STOCHASTIC convergence , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
In this paper, we propose several new iterative algorithms to solve the split feasibility problem in the Hilbert spaces. By virtue of new analytical techniques, we prove that the iterative sequence generated by these iterative procedures converges to the solution of the split feasibility problem which is the best close to a given point. In particular, the minimum-norm solution can be found via our iteration method. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
34. A selected method for the optimal parameters of the AOR iteration.
- Author
-
Ren, Luna, Ren, Fujiao, and Wen, Ruiping
- Subjects
- *
ITERATIVE methods (Mathematics) , *MATHEMATICAL optimization , *LINEAR systems , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
In this paper, we present an optimization technique to find the optimal parameters of the AOR iteration, which just needs to minimize the 2-norm of the residual vector and avoids solving the spectral radius of the iteration matrix of the SOR method. Meanwhile, numerical results are provided to indicate that the new method is more robust than the AOR method for larger intervals of the parameters ω and γ. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
35. Higher integrability of iterated operators on differential forms.
- Author
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Ding, Shusen, Shi, Guannan, and Xing, Yuming
- Subjects
- *
ITERATIVE methods (Mathematics) , *DIFFERENTIAL forms , *PROOF theory , *EMBEDDING theorems , *MATHEMATICAL inequalities , *MATHEMATICAL analysis - Abstract
In this paper, we first prove the local higher integrability and higher order imbedding theorems for the iterated operators defined on differential forms. Then, we prove the global higher integrability and higher order imbedding inequalities for these operators. Finally, we demonstrate applications of the main results by examples. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
36. Alternating-directional PMHSS iteration method for a class of two-by-two block linear systems.
- Author
-
Wang, Teng and Lu, Linzhang
- Subjects
- *
ITERATIVE methods (Mathematics) , *LINEAR systems , *NEWTON-Raphson method , *STOCHASTIC convergence , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
In Bai et al. (2013), a preconditioned modified HSS (PMHSS) method was proposed for a class of two-by-two block systems of linear equations. In this paper, the PMHSS method is modified by adding one more parameter in the iteration. Convergence of the modified PMHSS method is guaranteed. Theoretic analysis and numerical experiment show that the modification improves the PMHSS method. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
37. Weak sharpness for set-valued variational inequalities and applications to finite termination of iterative algorithms.
- Author
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Xiong, J. and Li, J.
- Subjects
- *
VARIATIONAL inequalities (Mathematics) , *ITERATIVE methods (Mathematics) , *ALGORITHMS , *MATHEMATICAL mappings , *MATHEMATICAL analysis - Abstract
In this paper, we introduce the notion of weak sharpness for set-valued variational inequalities in then-dimensional Euclidean space and then present some characterizations of weak sharpness. We also give some examples to illustrate this notion. Under the assumption of weak sharpness, by using the inner limit of a set sequence we establish a sufficient and necessary condition to guarantee the finite termination of an arbitrary algorithm for solving a set-valued variational inequality involving maximal monotone mappings. As an application, we show that the sequence generated by the hybrid projection-proximal point algorithm proposed by Solodov and Svaiter terminates at solutions in a finite number of iterations. These obtained results extend some known results of classical variational inequalities. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
38. The categories of flows of Set and Top
- Author
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Echi, Othman
- Subjects
- *
CATEGORIES (Mathematics) , *SET theory , *MATHEMATICAL analysis , *DYNAMICS , *COMPACT spaces (Topology) , *ITERATIVE methods (Mathematics) , *MORPHISMS (Mathematics) - Abstract
Abstract: Following John Kennison, a flow (or discrete dynamical system) in a category C is a couple , where X is an object of C and is a morphism, called the iterator. If and are flows in C, then is a morphism of flows from to if . We let denote the resulting category of flows in C. This paper deals with and , where Set and Top denote respectively the categories of sets and topological spaces. By a Gottschalk flow, we mean a flow in Top satisfying the following conditions: [(i)] If is any almost periodic point of f, then the closure is a minimal set of f; [(ii)] All points in any minimal set of f are almost periodic points. As proven by Gottschalk, if X is a compact Hausdorff space and is a continuous function, then is a Gottschalk flow. In this paper, we prove that for any flow of Set, there is a topology on X for which is a Gottschalk flow in Top. This, actually, defines a covariant functor from into . The main result of this paper provides a characterization of spaces in the image of the functor in order-theoretical terms. Some categorical properties of and are also given. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
39. Enhanced parallel cat swarm optimization based on the Taguchi method
- Author
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Tsai, Pei-Wei, Pan, Jeng-Shyang, Chen, Shyi-Ming, and Liao, Bin-Yih
- Subjects
- *
MATHEMATICAL optimization , *TAGUCHI methods , *ALGORITHMS , *TECHNOLOGY , *ITERATIVE methods (Mathematics) , *INDUSTRIES , *PARTICLE swarm optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we present an enhanced parallel cat swarm optimization (EPCSO) method for solving numerical optimization problems. The parallel cat swarm optimization (PCSO) method is an optimization algorithm designed to solve numerical optimization problems under the conditions of a small population size and a few iteration numbers. The Taguchi method is widely used in the industry for optimizing the product and the process conditions. By adopting the Taguchi method into the tracing mode process of the PCSO method, we propose the EPCSO method with better accuracy and less computational time. In this paper, five test functions are used to evaluate the accuracy of the proposed EPCSO method. The experimental results show that the proposed EPCSO method gets higher accuracies than the existing PSO-based methods and requires less computational time than the PCSO method. We also apply the proposed method to solve the aircraft schedule recovery problem. The experimental results show that the proposed EPCSO method can provide the optimum recovered aircraft schedule in a very short time. The proposed EPCSO method gets the same recovery schedule having the same total delay time, the same delayed flight numbers and the same number of long delay flights as the . The optimal solutions can be found by the proposed EPCSO method in a very short time. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
40. A GENERALIZED RANDOM NONLINEAR VARIATIONAL INCLUSION FOR MULTI-VALUED RANDOM OPERATORS IN A UNIFORMLY SMOOTH BANACH SPACE.
- Author
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Onjai-Uea, Nawitcha and Kumam, Poom
- Subjects
- *
RANDOM operators , *NONLINEAR statistical models , *VARIATIONAL inequalities (Mathematics) , *BANACH spaces , *ALGORITHMS , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICAL mappings - Abstract
In this paper, we introduce and study the random nonlinear variational inclusion problem with multi-valued random operators. We define a random iterative algorithm for finding the approximate solutions of class of random variational inclusions and establish the convergence of random iterative sequence generated by proposed algorithm in a uniformly smooth Banach space. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2012
41. Locally analytic functions in a local field of positive characteristic
- Author
-
Jeong, Sangtae
- Subjects
- *
ANALYTIC functions , *ALGEBRAIC fields , *CHARACTERISTIC functions , *PROOF theory , *ITERATIVE methods (Mathematics) , *CONTINUOUS functions , *MATHEMATICAL analysis - Abstract
Abstract: In a recent paper (Buium et al., 2011 ), Buium et al. proved that f is a locally analytic function from the p-adic integers, to itself if and only if it is written as a restricted power series over with finitely many iterates of the Fermat quotient operator. In this paper we establish the function field analogs of their result. In addition, we deduce Wagnerʼs result, which is the function field analog of Mahlerʼs result for continuous functions on . [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
42. An iterative thresholding algorithm for linear inverse problems with multi-constraints and its applications
- Author
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Khoramian, Saman
- Subjects
- *
ALGORITHMS , *INVERSE problems , *NUMERICAL analysis , *MATHEMATICAL analysis , *ITERATIVE methods (Mathematics) , *PROBLEM solving - Abstract
Abstract: In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. DeMol (2004) . This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
43. GMRES implementations and residual smoothing techniques for solving ill-posed linear systems
- Author
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Matinfar, M., Zareamoghaddam, H., Eslami, M., and Saeidy, M.
- Subjects
- *
GENERALIZED minimal residual method , *SMOOTHING (Numerical analysis) , *LINEAR systems , *STOCHASTIC convergence , *PROBLEM solving , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract: There are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
44. On a System of Nonlinear Variational Inclusions with Hh ?-Monotone Operators.
- Author
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Zeqing Liu, Ume, Jeong Sheok, and Kang, Shin Min
- Subjects
- *
NONLINEAR systems , *MONOTONE operators , *EXISTENCE theorems , *ITERATIVE methods (Mathematics) , *HILBERT space , *MATHEMATICAL analysis , *APPLIED mathematics - Abstract
This paper is concerned mainly with the existence and iterative approximation of solutions for a system of nonlinear variational inclusions involving the strongly Hh ?-monotone operators in Hilbert spaces. The results presented in this paper extend, improve, and unify many known results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
45. Some Aspects of Extended General Variational Inequalities.
- Author
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Noor, Muhammad Aslam
- Subjects
- *
VARIATIONAL inequalities (Mathematics) , *SENSITIVITY analysis , *ITERATIVE methods (Mathematics) , *OPERATOR theory , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Noor "Extended general variational inequalities," 2009, "Auxiliary principle technique for extended general variational inequalities," 2008, "Sensitivity analysis of extended general variational inequalities," 2009, "Projection iterative methods for extended general variational inequalities," 2010 introduced and studied a new class of variational inequalities, which is called the extended general variational inequality involving three different operators. This class of variational inequalities includes several classes of variational inequalities and optimization problems. The main motivation of this paper is to review some aspects of these variational inequalities including the iterative methods and sensitivity analysis. We expect that this paper may stimulate future research in this field along with novel applications. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
46. Parameterized collision region for centralized motion planning of multiagents along specified paths.
- Author
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Choi, Jeong S., Yoon, Younghwan, Choi, Myoung H., and Lee, Beom H.
- Subjects
- *
PARAMETER estimation , *COLLISIONS (Physics) , *MOTION , *MULTIAGENT systems , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICAL models - Abstract
This paper presents closed-form analytic solutions for collision detection among multiagents traveling along specified paths. Previous solutions for centralized multiagent systems have mainly used iterative computational approaches for collision detection, which impose a heavy computational burden on the systems. In this paper, we formalize a new mathematical approach to overcoming the difficulty on the basis of simple continuous curvature (SCC) path modeling and a collision representation tool, extended collision map (ECM) method. The formulation permits all the potential collisions to be detected, represented, and parameterized with physical and geometric variables. The proposed parameterized collision region (PCR) method is a simple but precise, computationally efficient tool for describing complicated potential collisions with time traveled. Several simulations are presented to validate the proposed approach for use in centralized collision detectors and to compare the results with those of the iterative computational method and the proximity query package (PQP) method that are available. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
47. Mathematical analysis to a nonlinear fourth-order partial differential equation
- Author
-
Liang, Bo
- Subjects
- *
PARTIAL differential equations , *MATHEMATICAL analysis , *FIXED point theory , *ITERATIVE methods (Mathematics) , *THIN films , *BOUNDARY value problems , *ESTIMATION theory - Abstract
Abstract: The paper first study the steady-state thin film type equation with Navier boundary conditions in multidimensional space. By the truncation method, a fixed point argument and some energy estimates, the existence and asymptotic limit for the positive weak solutions are given. Second, the parabolic equation with a Navier boundary in one-dimensional space is researched. The existence is obtained by applying a semi-discrete method for the time variable and solving the corresponding elliptic problem. The uniqueness is shown for depending on an energy estimate. In addition, the iteration relation of the semi-discrete problem gives an exponential decay result for the time . The thin film equation, which is usually used to describe the motion of a very thin layer of viscous in compressible fluids along an inclined plane, is a class of nonlinear fourth-order parabolic equations and the maximum principle does not hold directly. For applying the classic theory of partial differential equation, the paper transforms the fourth-order problem into a second-order elliptic–elliptic system or a second-order parabolic–elliptic system. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
48. Global existence and Mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations
- Author
-
Liu, Zeqing, Jiang, Anshu, Kang, Shin Min, and Ume, Jeong Sheok
- Subjects
- *
NUMERICAL solutions to delay differential equations , *EXISTENCE theorems , *ITERATIVE methods (Mathematics) , *NONLINEAR theories , *MATHEMATICAL analysis , *MATHEMATICAL physics , *FIXED point theory , *ERROR analysis in mathematics - Abstract
Abstract: This paper deals with the first order nonlinear neutral delay differential equationwhere and with lim t→+∞ σ l (t)=+∞ for l ∈{1,2,…, n}. By using the Banach fixed point theorem, we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p, construct some Mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions. Seven examples are presented to illuminate the results obtained in this paper. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
49. Modifications of higher-order convergence for solving nonlinear equations
- Author
-
Liu, Xi-Lan and Wang, Xiao-Rui
- Subjects
- *
STOCHASTIC convergence , *NUMERICAL solutions to nonlinear differential equations , *NEWTON-Raphson method , *MATHEMATICAL analysis , *ITERATIVE methods (Mathematics) - Abstract
Abstract: In [Liang Fang, Guoping He, Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations, J. Comput. Appl. Math. 228 (2009) 296–303], the authors pointed out that the iteration constructed in [Y.M. Ham, C.B. Chun and S.G. Lee, Some higher-order modifications of Newton’s method for solving nonlinear equations, J. Comput. Appl. Math. 222 (2008) 477–486] failed when . They gave some counterexamples and obtained a modified result. However, they did not show the essential reason which leads to the incorrect result. In this paper, we shall show that reason and present more general results than the above-mentioned papers. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
50. A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces
- Author
-
Chang, S.S., Joseph Lee, H.W., Chan, Chi Kin, and Liu, J.A.
- Subjects
- *
NUMERICAL solutions to nonlinear differential equations , *VARIATIONAL inequalities (Mathematics) , *BANACH spaces , *LYAPUNOV functions , *MATHEMATICAL analysis , *ITERATIVE methods (Mathematics) - Abstract
Abstract: The purpose of this paper is by using the generalized projection approach to introduce an iterative scheme for finding a solution to a system of generalized nonlinear variational inequality problem. Under suitable conditions, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces. The results presented in the paper improve and extend some recent results. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
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