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In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents a family of compensated algorithms to accurately evaluate a polynomial in Bernstein form with floating point coefficients. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. At each stage of computation, round-off error is passed on to first order errors, then to second order errors, and so on. After the computation has been "filtered" (K − 1) times via this process, the resulting output is as accurate as the de Casteljau algorithm performed in K times the working precision. Forward error analysis and numerical experiments illustrate the accuracy of this family of algorithms. [ABSTRACT FROM AUTHOR]

The solution of discrete ill-posed problems has been a subject of research for many years. Among the many methods described in the literature, the Bregman algorithm has attracted a great deal attention and been widely investigated. Recently, a nonstationary preconditioned version of this algorithm, referred to as the nonstationary modified linearized Bregman algorithm, was proposed. The aim of this paper is to discuss numerical aspects of this algorithm and to compare computed results with known theoretical properties. We also discuss the effect of several parameters required by the algorithm on the computed solution. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new numerical algorithm for solving the Riesz tempered space fractional diffusion equation. The stability and convergence of the numerical scheme are discussed via the technique of matrix analysis. Finally, numerical experiments are performed to confirm the effectiveness of our numerical algorithm. [ABSTRACT FROM AUTHOR]

The solution set of a system of polynomial equations, called an algebraic set, can be decomposed into finitely many irreducible components. In numerical algebraic geometry, irreducible algebraic sets are represented by witness sets, whereas general algebraic sets allow a numerical irreducible decomposition comprising a collection of witness sets, one for each irreducible component. We denote the solution set of any system of polynomials f : C N → C n as V ( f ) ⊂ C N . Given a witness set for some algebraic set Z ⊂ C N and a system of polynomials f : C N → C n , the algorithms of this paper compute a numerical irreducible decomposition of the set Z ∩ V ( f ) . While extending the types of intersection problems that can be solved via numerical algebraic geometry, this approach is also a unification of two existing algorithms: the diagonal intersection algorithm and the homotopy membership test. The new approach includes as a special case the “extension problem” where one wishes to intersect an irreducible component A of V ( g ( x ) ) with V ( f ( x , y ) ) , where f introduces new variables, y . For example, this problem arises in computing the singularities of A when the singularity conditions are expressed in terms of new variables associated to the tangent space of A . Several examples are included to demonstrate the effectiveness of our approach applied in a variety of scenarios. [ABSTRACT FROM AUTHOR]

In this paper, the authors developed a new differential quadrature method "exponential modified cubic B-spline differential quadrature method (Expo-MCB-DQM)” by using exponential modified cubic B-spline functions as test functions in the traditional differential quadrature method [32]. The new method is tested on one and two dimensional nonlinear Burgers’ equations. To check the efficiency and accuracy of the proposed method five numerical problems have been considered. The numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods. Stability analysis of the algorithm is also done by using matrix stability analysis method. [ABSTRACT FROM AUTHOR]

Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black–Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach. [Copyright &y& Elsevier]

Abstract: Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options. [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]

Abstract: In solid state physics, the most widely used techniques to calculate the electronic levels in nanostructures are the effective masses approximation (EMA) and its extension the multiband k · p method (see ). They have been particularly successful in the case of heterostructures (see, e.g. ). This paper discusses the multiscale analysis of the Schrödinger equation with rapidly oscillating coefficients. The new contributions obtained in this paper are the determination of the convergence rate for the approximate solutions, the definition of boundary layer solutions, and higher-order correctors. Consequently, a multiscale finite element method and some numerical results are presented. As one of the main results of this paper, we give a reasonable interpretation why the effective mass approximation is very accurate for calculating the band structures in semiconductor in the vicinity of Γ point, from the viewpoint of mathematics. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a heuristic algorithm, different from the Frank–Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a kind of univariate multiquadric (MQ) quasi-interpolation and use it to solve Burgers’ equation (with viscosity). At first we construct the MQ quasi-interpolation, which possesses the properties of linear reproducing and preserving monotonicity. Next we obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Then, we verify our method for two examples with distinguishing initial value condition. One example is tested for three Reynolds number, that is, R =10, R =100, and R =10,000. From the numerical experiments, we see that the presented method in this paper is valid although the accuracy of the technique is not higher than Hon and Mao’s one. Another example is used to examine the travelling of the shock. We can improve the accuracy by selecting an appropriate shape parameter and using a higher accurate MQ quasi-interpolation. The advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement. [Copyright &y& Elsevier]

Abstract: The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing quasi-Newton method for the solution of the nonlinear complementarity problems by constructing a new smoothing approximation function. Global and local superlinear convergence results of the proposed algorithm are established under suitable conditions. Some numerical results are reported in the paper. [Copyright &y& Elsevier]

This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability obtained by Ignatovand Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided. [ABSTRACT FROM AUTHOR]

Uncertain differential equation is a type of differential equation driven by Liu process and has been widely applied to many fields especially to uncertain finance. Unfortunately, the analytic solutions of uncertain differential equations cannot always be obtained. So far, some numerical methods have been investigated. This paper designs a new numerical algorithm for solving uncertain differential equations via Milne method. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a fractional thermal wave model for a bi-layered spherical tissue. Implicit finite difference method is employed to obtain the solution of the direct problem. The inverse analysis for simultaneously estimating the Caputo fractional derivative and the relaxation time parameters is implemented by means of the Levenberg–Marquardt method. Compared with the experimental data, we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment. We have also discussed the effect of the fractional derivative, the relaxation time parameters, the initial guess as well as the sensitivity problem. All the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new filled function, and give an efficient criterion to choose its two parameters appropriately. An algorithm for unconstrained global optimization is developed from this new filled function. numerical results with a comparison on many test problems show that this algorithm is efficient and reliable. [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]

A new definition of the filled function is presented in this paper. Based on the definition, a new filled function is presented, and a global optimization algorithm is developed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. The numerical experiments further show that the algorithm may solve higher dimensional global optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, a numerical power series algorithm which is based on the improved Taylor matrix method is introduced for the approximate solution of Abel-type differential equations and also, Riccati differential equations. The technique is defined and illustrated with some numerical examples. The obtained results reveal that the method is very effective, simple and valid high accuracy. The method can be easily extended to other nonlinear equations. [ABSTRACT FROM AUTHOR]

In the CQ-like algorithms for the split feasibility problem, in order to get the step-size, one has to compute the largest eigenvalue of the related matrix or use some line search scheme. Our contribution in this short note is to give a simple CQ-like algorithm in which the step-size is directly computed. The algorithm presented in this paper not only need not to compute the largest eigenvalue of the related matrix but also need not to use any line search scheme. The theoretical convergence and numerical results are also given. [ABSTRACT FROM AUTHOR]

The fractional-order total variation(TV) image denoising model has been proved to be able to avoid the “blocky effect”. However, it is difficult to be solved due to the non-differentiability of the fractional-order TV regularization term. In this paper, the proximity algorithm is used to solve the fractional-order TV optimization problem, which provides an effective tool for the study of the fractional-order TV denoising model. In this method, the complex fractional-order TV optimization problem is solved by using a sequence of simpler proximity operators, and therefore it is effective to deal with the problem of algorithm implementation. The final numerical procedure is given for image denoising, and the experimental results verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical method for computing the nearest low-rank correlation matrix (LRCM). Motivated by the fact that the nearest LRCM problem can be reformulated as a standard nonlinear equality constrained optimization problem with matrix variables via the Gramian representation, we propose a new algorithm based on the sequential quadratic programming (SQP) method. On each iteration, we do not solve the quadratic program (QP) corresponding to the exact Hessian, but a modified QP with a simpler Hessian. This QP subproblem can be solved efficiently by equivalently transforming it to a sparse linear system. Global convergence is established and preliminary numerical results are presented to demonstrate the proposed method is potentially useful. [ABSTRACT FROM AUTHOR]

Provided with the real spectrum, this paper presents a numerical procedure based on the induction principle to solve two types of inverse eigenvalue problems, one for nonnegative matrices and another for symmetric nonnegative matrices. As an immediate application, our approach can offer not only the sufficient condition to solve inverse eigenvalue problems for nonnegative or symmetric nonnegative matrices, but also a numerical way to solve inverse eigenvalue problems for stochastic matrices. Numerical examples are presented to show the capacity of our method. [ABSTRACT FROM AUTHOR]

Fast algorithms for solving symmetric penta-diagonal Toeplitz linear systems have been proposed in McNally (2010) [7], Nemani (2010) [8] and Xu (2010) [11]. In this paper, we discuss the general nonsymmetric problem and propose an algorithm for solving nonsymmetric penta-diagonal Toeplitz linear systems. Numerical examples are given to illustrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop dwindling filter idea and trust region strategy for solving nonlinear optimization. Compared with traditional filter trust region algorithm, the new filter algorithm has more flexibility for the acceptance of the trial step and the feasibility restoration phase is not needed. Under mild conditions, the global convergence of the new algorithm is analyzed. Preliminary numerical results are reported. [Copyright &y& Elsevier]

• The original identification model is decomposed into several sub models according to the dimension of output and different forms of parameters. • To solve the unmeasurable noise terms in the information matrices, we construct some auxiliary models based on the obtained parameter estimates. • To cut down the redundant estimates and solve the associate terms , a partially coupled nonlinear parameter optimization algorithm is proposed. A key to the analysis and design of a dynamic system is to establish a suitable mathematical model of the system. This paper investigates the parameter optimization problem of a class of radial basis function-based multivariate hybrid models. Taking into account the high dimensions of the models and different forms of the parameters, the original identification model is separated into several regressive sub-identification models according to the characteristics of model outputs. Some auxiliary models are constructed to solve the unmeasurable noise terms in the information matrices. For the purpose of eliminating the redundant computation and to deal with the associate terms caused by the model decomposition, inspired by the coupling concept, a partially-coupled nonlinear parameter optimization algorithm is proposed for the multivariate hybrid models. Through the computational efficiency analysis and numerical simulation verification, it is shown that the proposed algorithm has low computational complexity and high parameter estimation accuracy. [ABSTRACT FROM AUTHOR]

Abstract: Using trigonometric polynomial interpolation, a fast and effective numerical algorithm for computing the inverse of a triangular Toeplitz matrix with real numbers has been recently proposed (Lin et al., 2004) [7]. The complexity of the algorithm is two fast Fourier transforms (FFTs) and one fast cosine transform (DCT) of -vectors. In this paper, we present an algorithm with two fast Fourier transforms (FFTs) of -vectors for calculating the inverse of a triangular Toeplitz matrix with real and/or complex numbers. A theoretical accuracy and error analysis is also considered. Numerical examples are given to illustrate the effectiveness of our method. [Copyright &y& Elsevier]

Abstract: In this paper, based on a symmetrically perturbed smoothing Fischer–Burmeister function, a non-interior continuation method is proposed for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. Under monotonicity, it is shown that our algorithm is globally and locally superlinearly convergent without requiring strict complementarity assumption at the SOCCP solution. Furthermore, the proposed algorithm has local quadratic convergence under mild conditions. Some numerical results are reported which indicate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Jacobi–Stirling numbers of first and second kind and their corresponding associated matrices play an important role in Combinatorics. This paper presents an efficient method that guarantees that the computation of the singular values and the inverses of these matrices can be performed with high relative accuracy. Numerical examples are included. [Copyright &y& Elsevier]

Abstract: In this paper, a practical bivariate Newton–Thiele type matrix Padé approximation is introduced by using the generalized inverse of a matrix. The approximants are expressed in the form of Newton expansion and branched continued fractions, which can be computed by an efficient recursive algorithm. Some algebraic properties are also discussed and the application in state-space realization of the 2-D filters is given in the end. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the wave equations in perforated domains with a homogeneous Neumann condition on the boundary of the holes. The multiscale asymptotic expansion of the solution for the problem are constructed and associated explicit convergence rates are obtained. A multiscale numerical method is introduced. Finally, we present some numerical results which support strongly the convergence theorem. [Copyright &y& Elsevier]

In this paper, two explicit conversion formulae between triangular and rectangular Bézier patches are derived. Using the formulae, one triangular Bézier patch of degree n can be converted into one rectangular Bézier patch of degree n × n. And one rectangular Bézier patch of degree m × n can be converted into two triangular Bézier patches of degree m + n. Besides, two stable recursive algorithms corresponding to the two conversion formulae are given. Using the algorithms, when converting triangular Bézier patches to rectangular Bézier patches, we can computer the relations between the control points of the two types of patches for any based on the relationships for When converting rectangular Bézier patches to triangular Bézier patches, we can computer the relations between the control points of the two types of patches for any , and , based on the relationships for . [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the real eigenvalue bounds of standard and generalized real interval eigenvalue problems. Based on some known sufficient conditions for the regularity of interval matrices, a new algorithm for computing real eigenvalue bounds for real interval matrices is proposed. It can easily be extended for applying to generalized real interval eigenvalue problems. One advantage of the method is that the computation procedure takes less time than former methods we have proposed. Therefore it can be applied for solving larger interval eigenvalue problems. Finally, some numerical examples are presented which show the effectiveness of the method. [Copyright &y& Elsevier]

Abstract: In this paper, we concentrate on solving a convex time space network flow problem with decomposable structures. We first describe the convex time space network flow optimization model, and transform it into an equivalent variational inequality problem. Then, after exploring the decomposable structure of primal decision variables, we propose a novel decomposable self-adaptive projection-based prediction–correction algorithm (DSPPCA) to solve the model, and then further provide its convergent theory. Finally, we report the computational performances through computational experiments. Numerical results reveal that DSPPCA not only can enhance the accuracy and convergence rate significantly, but also can be a powerful search algorithm for convex optimization problems with decomposable structures of decision variables. [Copyright &y& Elsevier]

Abstract: In this paper, the generalized complementarity problem is studied. Based on a new smoothing function, the generalized complementarity problem is solved by a smoothing Newton-type algorithm. Under suitable conditions, we prove that the iteration sequence generated by the proposed smoothing method is bounded and the proposed algorithm is globally convergent. Some numerical results are reported. [Copyright &y& Elsevier]

Abstract: This paper deals with the null controllability of an initial-boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds. The control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small. We first prove that, if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition, the equations can be driven exactly to zero. We also present an iterative algorithm of the quasi-Newton kind for the computation of the control and we prove a convergence result. The behavior of this algorithm is illustrated with some numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the Cholesky decomposition of the Hermitian positive definite quaternion matrix. For the first time, the structure-preserving Gauss transformation is defined, and then a novel structure-preserving algorithm, which is applied to its real representation matrix, is proposed. Our algorithm needs only real number operations, does not depend on the quaternion toolbox for matlab (QTFM) and has more portability. Although the flops of our algorithm are theoretically about the same as those based on quaternion arithmetic operations or QTFM, numerical experiments show that our algorithm runs faster. [Copyright &y& Elsevier]

Abstract: This paper proposes an interactive approach for solving bi-level integer multi-objective fractional programming problem. At the first phase of the solution approach, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm then the two level decision makers use the Charnes and Cooper transformation to convert the fractional objective functions to equivalent linear functions. At the second phase, the algorithm simplifies the equivalent problem by transforming it into separate multi-objective decision-making problem and solving it by using the ε-constraint method. In addition, the theoretical results are illustrated with the help of a numerical example. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the convergence of the double-shift and multi-shift QR algorithms for symmetric tridiagonal matrices. We analyze how to choose multi-shifts by comparing the relationships between the number of iterations, CPU time and the number of multi-shifts. Numerical tests and figures are performed. [Copyright &y& Elsevier]

Abstract: In this paper, a restrained optimal perturbation method is firstly proposed to solve the backward heat conduction problem, the initial temperature distribution will be identified from the overspecified data, a regularization term is introduced in the objective functional for overcoming the ill-posedness of this problem, spectral projected gradient algorithm is used to solve the optimal problem, and we give the sensitivity analysis of the initial value. The results of numerical experiments are also presented. [Copyright &y& Elsevier]

Abstract: The linearized partial differential equation from the nonlinear partial differential equation which was proposed by Rudin, Osher and Fatemi [L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms] for solving image decomposition was introduced by Chambolle [A. Chambolle, An algorithm for total variation minimization and applications] and R. Acar and C.R. Vogel [R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems]. In this paper, we propose a method for solving the linearized partial differential equation and we show numerical results for denoising which demonstrate a significant improvement over other previous works. [Copyright &y& Elsevier]

Abstract: The 0-1 knapsack problem is an open issue in discrete optimization problems, which plays an important role in real applications. In this paper, a new bio-inspired model is proposed to solve this problem. The proposed method has three main steps. First, the 0-1 knapsack problem is converted into a directed graph by the network converting algorithm. Then, for the purpose of using the amoeboid organism model, the longest path problem is transformed into the shortest path problem. Finally, the shortest path problem can be well handled by the amoeboid organism algorithm. Numerical examples are given to illustrate the efficiency of the proposed model. [Copyright &y& Elsevier]

Abstract: In this paper, a boundary-type meshfree algorithm is proposed to accurately and stably deal with the two-dimensional inverse Stokes problems, which are highly ill-conditioned. Based on the Laplacian decomposition, the Stokes equations are recast as three Laplace equations. Then the modified collocation Trefftz method (MCTM), one of the most promising boundary-type meshless methods, is adopted to solve these three Laplace equations. The MCTM can stabilize the numerical scheme and obtain highly accurate results by utilizing the characteristic length. Accordingly, the numerical solutions of these three Laplace equations are expressed by linear combination of the modified T-complete functions. The unknown coefficients in the solution expressions are found by enforcing the satisfactions of the boundary conditions at the boundary collocation points. Three numerical examples are provided to show the efficacy and stability of the proposed meshless method. Besides, noises are added into the boundary conditions to demonstrate the stability of the proposed scheme for dealing with the inverse Stokes problems. [Copyright &y& Elsevier]

Abstract: In this paper, a trust-region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization. The most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase, a necessity in traditional filter methods. We solve quadratic programming subproblems based on the well-known Byrd–Omojokun trust-region method. Inexact solutions to these subproblems are allowed. Under some standard assumptions, global convergence of the proposed algorithm is established. Numerical results show our approach is potentially useful. [Copyright &y& Elsevier]

Abstract: In this paper we present a novel fast mesh parameterization algorithm based on subdivision scheme. First, an algorithm of approximating a given triangular mesh by the 4-point interpolatory subdivision is proposed, then a mesh parameterization method is developed based on the subdivision surface approximation algorithm. The novel mesh parameterization method is a generalization of the chordal parameterization to surface case, and it is more computationally efficient than previous methods because it obviates any computation of linear system of equations. Some numerical experiments show the efficiency of the novel algorithm. [Copyright &y& Elsevier]

Abstract: This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix . The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representations of the Moore–Penrose inverse, the weighted Moore–Penrose inverse, the Drazin inverse as well as and -inverses. Numerical examples on different test matrices are presented, as well as the comparison with well–known methods for generalized inverses computation. [Copyright &y& Elsevier]

Abstract: An adaptive parameter tuning of particle swarm optimization based on velocity information (APSO-VI) algorithm is proposed. In this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out, which reveals the reasons why PSO has relative poor global searching ability. Then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles. A new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control, which can avoid the velocity closed to zero at the early stage. Under the guide of the nonlinear ideal velocity, APSO-VI can maintain appropriate swarm diversity and alleviate the premature convergence validly. Numerical experiments are conducted to compare the proposed algorithm with different variants of PSO on some benchmark functions. Experimental results show that the proposed algorithm remarkably improves the ability of PSO to jump out of the local optima and significantly enhance the convergence speed and precision. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm reproducing conic sections and respecting the convexity properties of the initial data, is here presented. Significant numerical examples are included to illustrate the effectiveness of the proposed method and the smoothness of the limit curves. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method. [Copyright &y& Elsevier]