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The number of failed components in a failed or operating system is a very useful quantity in terms of replacement and maintenance strategies. These quantities have been studied in several papers for a system consisting of identical components. In this paper, the number of failed components at the time when the system fails and the number of failed components when the system is working are considered for a well-known and widely applicable k -out-of- n structure. The system is assumed to have multiple types of components. That is, the system consists of components having nonidentical failure time distributions. Optimization problems are also formulated to find optimal values of the number of components of each type, and the optimal replacement time. [ABSTRACT FROM AUTHOR]

Summary: This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers. [ABSTRACT FROM AUTHOR]

H-matrices play an important role in applied sciences such as numerical analysis and optimization theory. An attractive question is to identify whether a given matrix is an H-matrix. In this paper, we propose a new iterative algorithm for identifying H-matrices. We show that the proposed algorithm has linear convergence and can determine the H-matrix characterization for any given matrix. Its performance is illustrated in a set of numerical tests. [ABSTRACT FROM AUTHOR]

Concave knapsack problems with integer variables have many applications in real life, and they are NP-hard. In this paper, an exact and efficient algorithm is presented for concave knapsack problems. The algorithm combines the contour cut with a special cut to improve the lower bound and reduce the duality gap gradually in the iterative process. The lower bound of the problem is obtained by solving a linear underestimation problem. A special cut is performed by exploiting the structures of the objective function and the feasible region of the primal problem. The optimal solution can be found in a finite number of iterations, and numerical experiments are also reported for two different types of concave objective functions. The computational results show the algorithm is efficient. [ABSTRACT FROM AUTHOR]

In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF. [ABSTRACT FROM AUTHOR]

In this paper we extend our recently developed 2D adaptive factorization method for efficiently solving 3D inverse acoustic and electromagnetic scattering problems. Different from the previously used Simpson rule, we propose to use Gaussian quadrature rule, which provides improved reconstruction quality. Several numerical examples are presented to illustrate the effectiveness of our proposed adaptive method. To achieve better efficiency and robustness, we have based our implementation on the existing adaptive quadrature codes. [ABSTRACT FROM AUTHOR]

We consider the problem of tensor (i.e., multidimensional array) inpainting in this paper. By using higher-order singular value decomposition, we propose an iterative algorithm that performs soft thresholding on entries of the core tensor and then reconstructs via the directional orthogonal matrices. An inpainted tensor is obtained at the end of the iteration. Simulations conducted over color images, video frames, and MR images validate that the proposed algorithm is competitive with state-of-the-art completion algorithms. The evaluation is made in terms of quality metrics and visual comparison. [ABSTRACT FROM AUTHOR]

In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested to solve a class of complex matrix equations. With the real representation of a complex matrix as a tool, the sufficient and necessary conditions for the convergence factor are determined to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Also, we solve the problem which is proposed by Wu et al. (2010). Finally, some numerical examples are provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]

In this paper,we propose a new predictor–corrector interior-point method for symmetric cone programming. This algorithm is based on a wide neighbourhood and the Nesterov–Todd direction. We prove that, besides the predictor steps, each corrector step also reduces the duality gap by a rate of, whereris the rank of the associated Euclidean Jordan algebras. In particular, the complexity bound is, whereis a given tolerance. To our knowledge, this is the best complexity result obtained so far for interior-point methods with a wide neighbourhood over symmetric cones. The numerical results show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor-corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is established under the partially relaxed monotonicity assumption. As a consequence, the algorithm and results presented in the paper overcome incorrect algorithms and results existing in the literature. [ABSTRACT FROM AUTHOR]

Abstract: The system of equations arising in finite element simulations of components made of ferroelectroelastic materials is non-linear if the loading is sufficiently high. The Newton–Raphson method represents a widely used iterative technique to solve this system of non-linear equations. However, if the scalar potential formulation is utilised, convergence difficulties may occur. This circumstance can be primarily attributed to the specific form of the non-linear response of typical ferroelectroelastic materials being subjected to electrical loading. The present paper is devoted to modifications of the Newton–Raphson method, which are capable of improving the convergence behaviour experienced in the finite element iteration. We extend an existing modification to the fully coupled, ferroelectroelastic case. Additionally, a new modification of the Newton–Raphson method is proposed. This method applies an iteration algorithm, which is virtually equivalent to the iteration algorithm of the unmodified Newton–Raphson method combined with the vector potential formulation. An important feature of both modifications is that they are applied on the integration point level. Therefore, the global non-linear finite element iteration scheme remains unchanged. Finally, the practicability of the modifications discussed in the paper is shown in a numerical example. [Copyright &y& Elsevier]

In reliability analysis, computation of reliability index and finding design point is still a challenge. In this paper a new efficient reliability algorithm to locate design point is proposed. The proposed algorithm takes benefit from two significant means in its efficient search for the design point. One means is an updating rule by which the candidate of design point is updated and moved towards real design point. The criteria of updating in this rule are designed such that the candidate moves on an effective general path towards real design point. The other means is the introduction of a control parameter by which the search process at each iteration is limited to a relatively small region. This parameter controls the candidate of design point on its defined general path and does not let it leave the path. These two means have made the proposed algorithm very reliable in finding design point. Through numerical examples the accuracy and efficiency of the proposed algorithm is shown. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a new class of nonlinear mixed family of random fuzzy and crisp operator equation couples in fuzzy normed spaces based on the random version of the theory of (φ, ψ)-contractor due to Mihet. Further, some new random iterative algorithms for solving this kind of nonlinear operator equation couples in fuzzy normed spaces are constructed and the convergence of iterative sequences generated by the algorithms under joint orbitally complete conditions is proved. As applications, some new common fixed point theorems for a mixed family of fuzzy and crisp operators in fuzzy normed spaces are also given. The results presented in this paper improve and generalize the corresponding results of recent works. [ABSTRACT FROM AUTHOR]

A large number of algorithms for multidimensional signals processing and scientific computation come in the form of iterative stencil loops (ISLs), whose data dependencies span across multiple iterations. Because of their complex inner structure, automatic hardware acceleration of such algorithms is traditionally considered as a difficult task. In this paper, we introduce an automatic design flow that identifies, in a wide family of bidimensional data processing algorithms, subportions that exhibit a kind of parallelism close to that of ISLs; these are mapped onto a space of highly optimized ad-hoc architectures, which is efficiently explored to identify the best implementations with respect to both area and throughput. Experimental results show that the proposed methodology generates circuits whose performance is comparable to that of manually optimized solutions, and orders of magnitude higher than those generated by commercial high-level synthesis tools. [ABSTRACT FROM PUBLISHER]

In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradientcutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm. In the cyclic algorithm, using the known techniques, we can perform and develop practical numerical experiments. [ABSTRACT FROM AUTHOR]

Generating synthetic baseline populations is a fundamental step of agent-based modeling and simulation, which is growing fast in a wide range of socio-economic areas including transportation planning research. Traditionally, in many commercial and non-commercial microsimulation systems, the iterative proportional fitting (IPF) procedure has been used for creating the joint distribution of individuals when combining a reference joint distribution with target marginal distributions. Although IPF is simple, computationally efficient, and rigorously founded, it is unclear whether IPF well preserves the dependence structure of the reference joint table sufficiently when fitting it to target margins. In this paper, a novel method is proposed based on the copula concept in order to provide an alternative approach to the problem that IPF resolves. The dependency characteristic measures were computed and the results from the proposed method and IPF were compared. In most test cases, the proposed method outperformed IPF in preserving the dependence structure of the reference joint distribution. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed points of total asymptotically nonexpansive mappings in $\operatorname{CAT}(0)$ spaces. We also provide two examples to illustrate the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes. [ABSTRACT FROM AUTHOR]

The new non-iterative method of determining the dipole moment and location is presented in this paper. The algorithm of an object's localization and identification was achieved by using numerical calculations and approximation method. The arbitrary shapes of an object were assumed in the identification algorithm - axially symmetric spheroid (a prolate and an oblate). Several examples of localization and identification of an object's models were presented. Magnetic field of each object's model was calculated in Opera 3D program. An example of determining a missile's location and identification was presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial  filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper. [Copyright &y& Elsevier]

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]

Abstract: The existing algorithms for the minimum concave cost network flow problems mainly focus on the single-source problems. To handle both the single-source and the multiple-source problem in the same way, especially the problems with dense arcs, a deterministic annealing algorithm is proposed in this paper. The algorithm is derived from an application of the Lagrange and Hopfield-type barrier function. It consists of two major steps: one is to find a feasible descent direction by updating Lagrange multipliers with a globally convergent iterative procedure, which forms the major contribution of this paper, and the other is to generate a point in the feasible descent direction, which always automatically satisfies lower and upper bound constraints on variables provided that the step size is a number between zero and one. The algorithm is applicable to both the single-source and the multiple-source capacitated problem and is especially effective and efficient for the problems with dense arcs. Numerical results on 48 test problems show that the algorithm is effective and efficient. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a fast algorithm to solve the well known total variation (TV) inpainting model. Classically, the Euler–Lagrange equation deduced from TV inpainting model is solved by the gradient descent method and discretized by an explicit scheme, which produces a slow inpainting process. Sometimes an implicit scheme is also used to tackle the problem. Although the implicit scheme is several times faster than the explicit one, it is still too slow in many practical applications. In this paper, we propose to use an operator splitting method by adding new variables in the Euler–Lagrange equation of TV inpainting model such that the equation is split into a few very simple subproblems. Then we solve these subproblems by an alternate iteration. Numerically, the proposed algorithm is very easy to implement. In the numerical experiments, we mainly compare our algorithm with the existing implicit TV inpainting algorithms. It is shown that our algorithm is about ten to twenty times faster than the implicit TV inpainting algorithms with similar inpainting quality. The comparison of our algorithm with harmonic inpainting algorithm also shows some advantages and disadvantages of the TV inpainting model. [Copyright &y& Elsevier]

Abstract: In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20–30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi-ϕ-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45–57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11–20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257–266] and others. [Copyright &y& Elsevier]

Let A ∈ ℂN x N be a nonsingular complex matrix and b and c be complex vectors of length N. The goal of this paper is to investigate approaches for efficient approximations of the bilinear form c*A-1b. Equivalently, we wish to approximate the scalar value c*x, where x solves the linear system Ax = b. Here the matrix A can be very large or its elements can be too costly to compute so that A is not explicitly available and it is used only in the form of the matrix-vector product. Therefore a direct method is not an option. For A Hermitian positive definite, b*A-1b can be efficiently approximated as a by-product of the conjugate-gradient iterations, which is mathematically equivalent to the matching moment approximations computed via the Gauss-Christoffel quadrature. In this paper we propose a new method using the biconjugate gradient iterations which is applicable to the general complex case. The proposed approach will be compared with existing ones using analytic arguments and numerical experiments. [ABSTRACT FROM AUTHOR]

This paper concerns numerical methods for computing complex geometrical optics (CGO) solutions to the conductivity equation ∇ ⋅ σ∇u (⋅, k) = 0 in ℝ² for piecewise smooth conductivities σ, where k is a complex parameter. The key is to solve an R-linear singular integral equation defined in the unit disk. Recently, Astala et al. [Appl. Comput. Harmon. Anat., 29 (2010), pp. 2-17] proposed a complicated method for numerical computation of CGO solutions by solving a periodic version of the ℝ-linear integral equation in a rectangle containing the unit disk. In this paper, based on the fast algorithms in [P. Daripa and D. Mashat, Numer. Algorithms, 18 (1998), pp. 133-157] for singular integral transforms, we propose a simpler numerical method which solves the ℝ-linear integral equation in the unit disk directly. For the resulting ℝ-linear operator equation, a minimal residual iterative method is proposed. Numerical examples illustrate the accuracy and efficiency of the new method. [ABSTRACT FROM AUTHOR]

This paper deals with novel mathematical methods to locate the edges of heated planar objects employing simple photodiodes. Thereby, both the lateral edge position and the axial distance of the object can be determined. Furthermore, a method which allows the estimation of the rotation angle of the investigated object is discussed. In contrast to an infrared camera, photodiodes and the required electronic components are insensitive to mechanical vibrations commonly experienced in industrial fabrication processes. Nevertheless, the limited spatial resolution of such photodiode ensemble demands for a signal-processing-based resolution enhancement, which is presented in this paper. By means of simulation results, the efficiency of the novel methods is verified. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we compute and manipulate the support of monomial resolutions based on iterated mapping cones. We derive in this way algorithms to obtain homological and numerical invariants of monomial ideals without actually computing their resolution. Our computations include Betti diagrams, Hilbert series and irreducible decompositions. The algorithms derived by the method presented in the paper are efficient in practice as shown by experiments. [Copyright &y& Elsevier]

We give an explicit Krasnoselski-Mann type method for finding common solutions of the following system of equilibrium and hierarchical fixed points: {G(x*,y) ≥0, ∀x ϵFix(T), find x* ϵ Fix(T) such that ⟨X* - ƒ (x*), x - x*⟨ ≥ 0, ∀x ϵFix(T), where C is a closed convex subset of a Hilbert space H, G : C × C →ℝ is an equilibrium function, T : C → C is a nonexpansive mapping with Fix(T) its set of fixed points and ƒ : C → C is a ρ-contraction. Our algorithm is constructed and proved using the idea of the paper of [Y. Yao and Y.-C. Liou, 'Weak and strong convergence of Krasnosel'skiĭ-Mann iteration for hierarchical fixed point problems', Inverse Problems 24 (2008), 501-508], in which only the variational inequality problem of finding hierarchically a fixed point of a nonexpansive mapping T with respect to a ρ-contraction ƒ was considered. The paper follows the lines of research of corresponding results of Moudafi and Théra. [ABSTRACT FROM AUTHOR]

As a solution to the frequently reported problem of the high frequencies reconstructed sometimes many iterations after the low frequencies in tomography, we proposed in a recent paper [V. Israel-Jost, Ph. Choquet, and A. Constantinesco, Int. J. Biomed. Imaging, 2006, paper 34043.] a general adaptation that can apply to many algorithms: the incomplete backprojection. We stressed the fact that this type of frequency adapted (FA) algorithm works only when the linear problem of tomography to be solved involves deblurring, i.e., when the point spread functions (PSFs) associated with each voxel are large. Thus, depending on the desired level of detail, a parameter is set to achieve the reconstruction within a small number of iterations. The aim of this paper is to give a mathematical analysis of both the acceleration obtained and the convergence of an FA algorithm derived from the simultaneous algebraic reconstruction technique (SART) algorithm of Andersen and Kak, the so-called FA-SART algorithm. [ABSTRACT FROM AUTHOR]

The paper discusses several versions of the method of shortest residuals, a specific variant of the conjugate gradient algorithm, first introduced by Lemaréchal and Wolfe and discussed by Hestenes in a quadratic case. In the paper we analyze the global convergence of the versions considered. Numerical comparison of these versions of the method of shortest residuals and an implementation of a standard Polak–Ribière conjugate gradient algorithm is also provided. It supports the claim that the method of shortest residuals is a viable technique, competitive to other conjugate gradient algorithms. [ABSTRACT FROM AUTHOR]

One-step finite element method (also called inverse approach) is more and more widely used in the automobile industry because of its unique advantages. Initial solution is an essential issue to ensure the success of the non-linear resolution in the implicit static one-step finite element solver. In order to speed up the convergence of the Newton–Raphson iterations, different kinds of initial solution methods are known. These are studied and compared in this paper. Several examples are followed to show their performance and efficiency. However most of these methods are based on geometric considerations like the geometric mapping method or the radial length development method. This kind of geometry based mapping methods could not reflect all aspects of the actual forming process. Therefore, an energy based mapping algorithm was implemented and coupled with the reverse deformation method which is based on the assumption of linear elastic deformation. This novel algorithm is proposed to provide the initial solution of one-step finite element method. For a complicated sheet forming modeling initial solutions obtained by different energy based algorithms coupled with the reverse deformation method are then compared in this paper. The results show that the Desbrun quadratic energy method and the accordant parameterization method combined with the inverse deformation method respectively are universal, efficient and robust initial solution schemes for the one-step finite element method. [Copyright &y& Elsevier]

This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources. [ABSTRACT FROM AUTHOR]

Background: The tools and techniques used in morphometrics have always aimed to transform the physical shape of an object into a concise set of numerical data for mathematical analysis. The advent of landmark-based morphometrics opened new avenues of research, but these methods are not without drawbacks. The time investment required of trained individuals to accurately landmark a data set is significant, and the reliance on readily-identifiable physical features can hamper research efforts. This is especially true of those investigating smooth or featureless surfaces. Methods: In this paper, we present a new method to perform this transformation for data obtained from high-resolution scanning technology. This method uses surface scans, instead of landmarks, to calculate a shape difference metric analogous to Procrustes distance and perform superimposition. This is accomplished by building upon and extending the Iterative Closest Point algorithm. We also explore some new ways this data can be used; for example, we can calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we briefly demonstrate this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Trust region methods are a class of numerical methods for optimization. Unlike line search type methods where a line search is carried out in each iteration, trust region methods compute a trial step by solving a trust region subproblem where a model function is minimized within a trust region. Due to the trust region constraint, nonconvex models can be used in trust region subproblems, and trust region algorithms can be applied to nonconvex and ill-conditioned problems. Normally it is easier to establish the global convergence of a trust region algorithm than that of its line search counterpart. In the paper, we review recent results on trust region methods for unconstrained optimization, constrained optimization, nonlinear equations and nonlinear least squares, nonsmooth optimization and optimization without derivatives. Results on trust region subproblems and regularization methods are also discussed. [ABSTRACT FROM AUTHOR]

The vector iteration methods are one of the fundamental equation solving methods among eigenproblem solving methods; however, convergence to a specific mode is difficult in such methods. In this paper, a method is presented for double layer grid structures in which the vector iteration methods converge to the dominant modes. For obtaining the dominant modes, the starting iteration vector is optimized using genetic algorithm based on the mass participation ratio. Subsequently, (in order to obtain the upper dominant modes) the Gram-Schmidt orthogonalization method is used. The numerical results demonstrate the computational advantages of the proposed methodology. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, based on GCRS algorithm in Zhang and Zhao (2010) and the ideas in Gu et al. (2007), we present an improved generalized conjugate residual squared (IGCRS) algorithm that is designed for distributed parallel environments. The new improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS algorithm in such a way that all inner products per iteration are independent so that communication time required for inner products can be overlapped with useful computation. Theoretical analysis and numerical comparison of isoefficiency analysis show that the IGCRS method has better parallelism and scalability than the GCRS method, and the parallel performance can be improved by a factor of about 2. Finally, some numerical experiments clearly show that the IGCRS method can achieve better parallel performance with a higher scalability than the GCRS method and the improvement percentage of communication is up to 52.19% averagely, which meets our theoretical analysis. [Copyright &y& Elsevier]

The paper presents the iterative solutions of two coefficient inverse problems (CIPs) arising in frequency sounding and electrical prospecting. An iterative algorithm is constructed to obtain such solutions. Exploiting the Beilina–Klibanov approach to CIPs, this algorithm possesses the new iterative and refinement procedures. These features enhance significantly both the spatial and contrast resolutions of reconstructed coefficients. The computational effectiveness of the proposed numerical technique is demonstrated in computational experiments with two applied CIPs: electromagnetic or acoustic frequency sounding and electrical prospecting of layered media. The Slichter–Langer–Tikhonov formulation is exploited as a mathematical model of the latter. [ABSTRACT FROM PUBLISHER]

In this paper, a two-level defect-correction Oseen iterative finite element method is presented for the stationary conduction–convection equations based on local Gauss integration. The method combines the defect-correction method, the two-level strategy, and the locally stabilized method. The stability and convergence of the proposed method are deduced. Finally, numerical examples verify the theoretical results of the proposed algorithm and show that it is highly efficient and reliable for the considered problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a reweighted nuclear norm minimization algorithm based on the weighted fixed point method (RNNM–WFP algorithm) to recover a low rank matrix, which iteratively solves an unconstrained minimization problem introduced as a nonconvex smooth approximation of the low rank matrix minimization problem. We prove that any accumulation point of the sequence generated by the RNNM–WFP algorithm is a stationary point of the minimization problem. Numerical experiments on randomly generated matrix completion problems indicate that the proposed algorithm has better recoverability compared to existing iteratively reweighted algorithms. [Copyright &y& Elsevier]

This paper deals with the problem of finding minimum-norm fixed point of nonexpansive mappings. We present two types of iteration methods (one is implicit, and the other is explicit). We establish strong convergence theorems for both methods. Some applications are given regarding convex optimization problems and split feasibility problems. These results improve some known results existing in the literatures. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple, iteration free and easy-to-implement numerical algorithm for the solution of inverse Cauchy problem in linear or nonlinear elasticity. The bottom of a finite rectangular plate is imposed by overspecified boundary data, and we seek unknown data on the top side. A spring-damping transform method (SDTM) is introduced to the Navier equations, such that after a discretization by the differential quadrature method, we can apply a novel Lie-group integrator, namely the mixed group-preserving scheme (MGPS), to solve them as an initial value problem. Several numerical examples including nonlinear ones are examined to show that the MGPS can overcome the ill-posed behaviour of the inverse Cauchy problem in elasticity, which has good efficiency and stability against the noisy disturbance, even with an intensity large up toand. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the order of convergence and the efficiency of four families of iterative methods using frozen divided differences. The first two families correspond to a generalization of the secant method and the implementation made by Schmidt and Schwetlick. The other two frozen schemes consist of a generalization of Kurchatov method and an improvement of this method applying the technique used by Schmidt and Schwetlick previously. An approximation of the local convergence order is generated by the examples, and it numerically confirms that the order of the methods is well deduced. Moreover, the computational efficiency indexes of the four algorithms are presented and computed in order to compare their efficiency. [ABSTRACT FROM AUTHOR]

Normalization is a fundamental ring-theoretic operation; geometrically it resolves sin-gularities in codimension one. Existing algorithmic methods for computing the normal-ization rely on a common recipe: successively enlarge the given ring in form of an endo-morphism ring of a certain (fractional) ideal until the process becomes stationary. While Vasconcelos' method uses the dual Jacobian ideal, Grauert-Remmert-type algorithms rely on so-called test ideals. For algebraic varieties, one can apply such normalization algorithms globally, locally, or formal analytically at all points of the variety. In this paper, we relate the number of iterations for global Grauert-Remmert-type normaliza-tion algorithms to that of its local descendants. We complement our results by a study of ADE singularities. All intermediate singularities occurring in the normalization pro-cess are determined explicitly. Besides ADE singularities the process yields simple space curve singularities from the list of Friihbis-Kriiger. [ABSTRACT FROM AUTHOR]

In this paper, we develop a modified gradient based algorithm for solving matrix equations AXB + CXTD = F. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we propose a regularization of general Tikhonov type for large-scale ill-posed problems. We introduce the projection method of iterative bidiagonalization and show that the regularization parameter can be chosen without prior knowledge of the noise variance by using the method of balancing principle. An algorithm implicate the efficient numerical realization of the new choice rule. Numerical experiments for severely ill-show benchmark inverse problems show that new method is effective compared with other criterions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an efficient design algorithm is proposed to design the recently introduced two-dimensional (2D) critically sampled modified DFT (MDFT) modulated filter bank. First of all, the original perfect-reconstruction (PR) condition in frequency-domain of the filter bank is transformed into a spatial-domain condition, which is a set of quadratic equations with respect to the prototype filter (PF). Then, with the derived PR equations, the design problem is formulated into an unconstrained optimization problem that involves PR condition and stopband energy of the PF. An iterative algorithm is proposed to solve the optimization problem. The convergence of the algorithm is proved. Numerical results and comparison with existing method are included to show the effectiveness of the proposed design algorithm. [Copyright &y& Elsevier]