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Abstract: In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In the first part an solver for a semiseparable matrix of semiseparability rank p is derived, and in a second part we derive an solver for a band matrix with bandwidth . Both solvers are constructed in a similar way: firstly a Yule–Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side. Finally, a combination of the above methods is presented to solve linear systems with semiseparable plus band coefficient matrices. The overall complexity of this solver is plus lower order terms. In the final section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods. [Copyright &y& Elsevier]

Abstract This paper suggests a novel continuous-time gradient descent algorithm of a constrained convex unknown function with a stochastic noise in the observed data. The penalty function approach is employed to introduce the restrictions of the system and to provide a successful optimization process. The solution is restricted to a static scheme dealing with the class of strongly convex functions subject to a set of constraints. To estimate the stochastic gradient we employ a modified version of the synchronous detection method. All the parameters of the proposed approach are decreasing in time to both compensate noise effect in the observations and to provide the mean-square convergence of the suggested approach. We present two different numerical examples to validate the contributions of the paper. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new viscosity iterative method minimization algorithm for image restoration algorithm is proposed. Based on a new viscosity iteration, the algorithm for finding the common zeros of two accretive operators in the framework of uniformly smooth Banach spaces. Moreover, the strong convergence theorems for the iterative algorithms and an example is proposed which shows the validity of main theorem are proved. The results of this paper are improved and extended of the corresponding ones announced by many others and we also applied our result to solve a convex minimization problem and Gâteaux differentiable E P s and Variational Inequality. Experiment results show that the proposed algorithms outperform some other methods. Finally, we give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for applying to solve the image deblurring and image recovery problems. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a simplified reproducing kernel method to solve the linear Volterra integral equations with variable coefficients. The main idea of the method is to establish a reproducing kernel direct space that can be used in Volterra integral equations. And in the first time, this paper analyzes the convergence order and stability of the approximate solution. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and is not less than the second order convergence. The algorithm is proved to be feasible and stable through some numerical examples. [ABSTRACT FROM AUTHOR]

In the paper the author presents a novel kind of the WZ factorization algorithm, namely a block WZ factorization algorithm. The aim of this new algorithm is to utilize the computational power of contemporary computers with hierarchical memory. In the paper, some properties of the matrix Z are given and analyzed. Next, a version of the block WZ factorization is presented. The author shows that such a block WZ factorization exists for strictly diagonally dominant matrices. The computational cost of this block algorithm is presented. The time and the accuracy of proposed block WZ factorization algorithm for random dense square diagonally dominant matrices are reported. The block algorithm turned out to be faster even up to 300 times than the original WZ factorization. [ABSTRACT FROM AUTHOR]

In previous papers, the authors introduced and characterized a class of matrices called { K , s + 1 } -potent. Also, they established a method to construct these matrices. The purpose of this paper is to solve the associated inverse problem. Several algorithms are developed in order to find all involutory matrices K satisfying K A s + 1 K = A for a given matrix A ∈ C n × n and a given natural number s . The cases s = 0 and s ≥ 1 are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods. [ABSTRACT FROM AUTHOR]

In this paper we present an efficient framework for the evaluation of subdivision schemes with polynomial reproduction property. For all interested rational parameters between 0 and 1 with the same denominator, their exact limit positions on the subdivision curve can be obtained by solving a system of linear equations. When the framework is applied to binary and ternary 4-point interpolatory subdivision schemes, we find that the corresponding coefficient matrices are strictly diagonally dominant, and so the evaluation processes are robust. For any individual irrational parameters between 0 and 1, its approximate value is computed by a recursive algorithm which can attain an arbitrary error bound. For surface schemes generalizing univariate subdivision schemes with polynomial reproduction property, exact evaluation methods can also be derived by combining Stam’s method with that of this paper. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid algorithm of Nelder–Mead and scatter search algorithms called SSNM. Numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem. This paper also has a considerable contribution to the joint economic lot sizing (JELS) problem literature. This problem is considered for a two-stage supply chain with price-sensitive demand for geometric, geometric-then-equal size and optimal shipment policies. Solution procedures are also developed which use the SSNM algorithm in their steps. These models and solution procedures are novel in the JELS literature. [ABSTRACT FROM AUTHOR]

To find new solutions through the information provided by previously found solution(s), this paper is first to develop a new singular transform to change the local basin-barrier structure of the original problem in an infinite-dimensional space and then to propose an augmented partial Newton method to solve the transformed problem on the solution set. Mathematical justifications of the new formulation and method are established. Details on algorithm implementation are presented. Examples for two very different variational PDE problems are carried out to illustrate the method. Their numerical results are displayed by profile–contour plots and error/convergence data. The formulation and method developed in this paper can also be applied to solve multiple fixed point problems. [ABSTRACT FROM AUTHOR]

This paper presents an accurate implicit re-initialization approach in the framework of a level set method. The improved method includes two schemes for keeping the zero level set unperturbed. The first scheme is to derive and use a new formula for the smoothing parameter in the conventional re-initialization equation based on the principle of the interface not moving. The second scheme is to reduce the local time step to avoid the interface moving across grid points when the sign of the level set function near the interface is changed. The example presented suggests that the new algorithm has a better approximation to the signed distance function and obtains a more accurate interface than the algorithm presented by Sussman et al. (1994). For shape and topology optimization of fluid, the effectiveness of the developed method in this paper was demonstrated by the internal and external flow examples. [ABSTRACT FROM AUTHOR]

In this paper new algorithms are being proposed for evaluation of highly oscillatory integrals (HOIs) with stationary point(s). The algorithms are based on modified Levin quadrature (MLQ) with multiquadric radial basis functions (RBFs) coupled with quadrature rules based on hybrid functions of order 8 (HFQ8) and Haar wavelets quadrature (HWQ) (Aziz et al. 2011). Part of the new procedure presented in this paper is comprised of transplanting monomials (which are used in the conventional Levin method) by the RBFs. The linear and Hermite polynomials based quadratures (Xiang, 2007) are being replaced by the new methods based on HWQ and HFQ8 respectively. Both the methods are merged with MLQ to obtain the numerical solution of highly oscillatory integrals having stationary points. The accuracy of the new methods is neither dampened by presence of the stationary point(s) nor by the large value of frequency parameter ω . Theoretical facts about the error analysis of the new methods are analyzed and proved. Numerical examples are included to show efficiency and accuracy of the new methods. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding poles of rational functions from function values on open curves in the complex plane. For this problem, Nara and Ando recently proposed an algorithm that reduces the problem to a system of linear equations through contour integration. The main aim of this paper is to analyze and improve this algorithm by giving a new interpretation to the algorithm in terms of orthogonal polynomials. It is demonstrated that the system of linear equations is not always uniquely solvable and that this difficulty can be remedied by doubling the number of the linear equations. Moreover, to cope with discretization errors caused by numerical integration, we introduce new polynomials similar, in spirit, to discrete orthogonal polynomials, which yield an algorithm free from discretization errors. [ABSTRACT FROM AUTHOR]

In this paper, using the properties of graph convergence of H(.,.)-accretive operators, we construct a perturbed algorithm for solving systems of ill-posed variational inclusions involving H(.,.)-accretive operators. Under some suitable conditions, we prove that the sequence generated by the proposed method is strongly convergent to the unique solution of the problem. The main results presented in this paper generalize and improve some recent results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents two different versions of an optimal control method for enforcing mass conservation in level set algorithms. The proposed PDE-constrained optimization procedure corrects a numerical solution to the level set transport equation so as to satisfy a conservation law for the corresponding Heaviside function. In the original version of this method, conservation errors are corrected by adding the gradient of a scalar control variable to the convective flux in the state equation. In the present paper, we investigate the use of vector controls. The alternative formulation offers additional flexibility and requires less regularity than the original method. The nonlinear system of first-order optimality conditions is solved using a standard fixed-point iteration. The new methodology is evaluated numerically and compared to the scalar control approach. [Copyright &y& Elsevier]

Abstract: Theoretical analyses of algorithms are important to understand their search behaviors and develop more efficient algorithms. Compared with the plethora of works concerning the empirical study of the differential evolution (DE), little theoretical research has been done to investigate the convergence properties of DE so far. This paper focuses on theoretical researches on the convergence of DE and presents a convergent DE algorithm. First of all, it is proved that the classical DE cannot converge to the global optimal set with probability 1 by using the property that it cannot escape from a local optimal set. Inspired by the characteristics of the elitist genetic algorithm, this paper proposed a modified DE to overcome the disadvantage. The proposed algorithm employs two operators that assist it in escaping from a local optimal set and enhance the diversity of the population. And it is then verified that the proposed algorithm is capable of converging to global optima with probability 1. The theoretical research of this paper is undertaken in a finite discrete set, and the analysis tool used is the Markov chain. The numerical experiments are conducted on a deceptive function and a set of benchmark functions. The experimental results support the theoretical analyses on the convergence performances of the classical and modified DE algorithm. [Copyright &y& Elsevier]

Powell (1984) and Dai (2003) constructed respectively a counterexample to show that the Polak–Ribière–Polyak (PRP) conjugate gradient algorithm fails to globally converge for nonconvex functions even when the exact line search technique is used, which implies similar failure of the weak Wolfe–Powell (WWP) inexact line search technique. Does another inexact line search technique exist that can ensure global convergence for nonconvex functions? This paper gives a positive answer to this question and proposes a modified WWP (MWWP) inexact line search technique. An algorithm is presented that uses the MWWP inexact line search technique; the next point x k + 1 generated by the PRP formula is accepted if a positive condition holds, and otherwise, x k + 1 is defined by a technique for projection onto a parabolic surface. The proposed PRP conjugate gradient algorithm is shown to possess global convergence under inexact line search for nonconvex functions. Numerical performance of the proposed algorithm is shown to be competitive with those of similar algorithms. • A convex parabolic surface for projection is defined and a projection PRP algorithm is proposed. • Any unsatisfactory iteration points are projected onto this convex parabolic surface to get good points. • The PRP conjugate gradient algorithm for general functions under inexact line search is obtained. • Competitive numerical results are reported to show the good performance of the new algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the convergence of several optimize-then-discretize and discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimal control problems. To ensure the convergence of a discretize-then-optimize algorithm, one well-accepted criterion is to design the discretization scheme such that the resulting discretize-then-optimize algorithm commutes with the corresponding optimize-then-discretize algorithm. In other words, both algorithms should give rise to exactly the same discrete optimality system. However, such a restrictive criterion is not trivial to fulfill. By investigating a distributed control problem governed by an elliptic equation, we first show that enforcing such a stringent condition of commutative property is only sufficient but not necessary for achieving the desired convergence. We then introduce some suitable H 1 semi-norm penalty/regularization terms to recover the lost convergence due to the inconsistency caused by the loss of commutativity. Numerical experiments are carried out to verify our theoretical analysis and also validate the effectiveness of our proposed regularization techniques. [ABSTRACT FROM AUTHOR]

Registration refers to the useful process of aligning two similar but different intensity image functions in order to either track changes or combine information. Variational models are capable of finding transform maps containing large and non-uniform deformations between such a pair of images. Since finding a transform map is an inverse problem, as with all models, suitable regularisation is necessary to overcome the non-uniqueness of the problem. In the case of diffusion type models regularisation terms impose smoothness on the transformation by minimising the gradient of the flow field. The diffusion model also coincides with the basic model for optical flow frameworks of Horn and Schunck (1981). The biggest drawback with variational models is the large computational cost required to solve the highly non-linear system of PDEs; Chumchob and Chen (2011) developed a non-linear multigrid (NMG) method to address this cost problem. However, a closer look at the analysis of the NMG scheme highlighted omissions which affected the convergence of the NMG scheme. Moreover, the NMG method proposed by Chumchob and Chen did not impose any control of non-physical folding which invalidates a map. This paper has proposed several key ideas. First we re-evaluate the analysis of the NMG method to show how the omissions in Chumchob and Chen (2011) have a noticeable impact on the convergence of the NMG method. In addition, we also provide a way of estimating the convergence rate of a solver on the coarsest grid in order to estimate the number of iterations that will be required to obtain a solution with appropriate accuracy. Second we propose an extension to the Chumchob–Chen NMG method which controls any folding within the deformation. Experimental results on the proposed multigrid framework demonstrate improvements in convergence and the accuracy of registrations compared with previous methods. [ABSTRACT FROM AUTHOR]

In this paper an improved version of a verification algorithm for solving nonlinear systems of equations based on Krawczyk operator is presented. Compared with the original algorithm, the improved verification algorithm not only saves computing time, but also computes a narrower (or at least the same) inclusion of the solution to nonlinear systems of equations for certain classes of problems. Numerical results demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The reduction of a matrix to an upper J -Hessenberg form is a crucial step in the S R -algorithm (which is a Q R -like algorithm), structure-preserving, for computing eigenvalues and vectors, for a class of structured matrices. This reduction may be handled via the algorithm JHESS or via the recent algorithm JHMSH and its variants. The main drawback of JHESS (or JHMSH) is that it may suffer from a fatal breakdown, causing a brutal stop of the computations and hence, the S R -algorithm does not run. JHESS may also encounter near-breakdowns, source of serious numerical instability. In this paper, we focus on these aspects. We first bring light on the necessary and sufficient condition for the existence of the S R -decomposition, which is intimately linked to J -Hessenberg reduction. Then we will derive a strategy for curing fatal breakdowns and also for treating near breakdowns. Hence, the J -Hessenberg form may be obtained. Numerical experiments are given, demonstrating the efficiency of our strategies to cure and treat breakdowns or near breakdowns. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an effective method based upon the piecewise homotopy perturbation method (PHPM) is proposed for finding the numerical solutions of Fredholm integro-differential equations with weakly singular kernels. For these equations, the traditional homotopy perturbation method is divergent. So we present a modified homotopy perturbation method for solving this kind of equation. The advantages of the approach of this paper lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Two examples are given to show the effectiveness and convenience of this method. [Copyright &y& Elsevier]

Abstract: In the framework of dependent risks it is a crucial task for risk management purposes to quantify the probability that the aggregated risk exceeds some large value . Motivated by Asmussen et al. (2011) [1] in this paper we introduce a modified Asmussen–Kroese estimator for simulation of the rare event that the aggregated risk exceeds . We show that in the framework of log-Gaussian risks our novel estimator has the best possible performance i.e., it has asymptotically vanishing relative error. For the more general class of log-elliptical risks with marginal distributions in the Gumbel max-domain of attraction we propose a modified Rojas-Nandayapa estimator of the rare events of interest, which for specific importance sampling densities has a good logarithmic performance. Our numerical results presented in this paper demonstrate the excellent performance of our novel Asmussen–Kroese algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a new curve subdivision algorithm called interproximate subdivision for generating curves that interpolate some given vertices and approximate the other vertices. By the interproximate subdivision, only the vertices specified to be interpolated are fixed and the other vertices are updated at each refinement step. The refinement rules are derived to ensure that the eigenvalues of the refinement matrix satisfy the necessary condition of continuity. The interproximate subdivision also contains tension parameters assigned to vertices or edges for shape adjustment. Compared to the 4-point interpolatory subdivision scheme, the interproximate subdivision does not force the new inserted vertices to be interpolated and is thus expected to have improved behavior; and compared to the cubic -spline refinement scheme, the interproximate subdivision is able to generate curves interpolating user-specified vertices. In addition, the paper also presents two extensions of the interproximate subdivision: one automatically adapts the tension parameters locally according to the geometry of the control polygon during the refinement to achieve convexity preservation and the other automatically relaxes the interpolating property of some vertices to achieve better shape behavior. [Copyright &y& Elsevier]

Abstract: This paper reports on improvements to recent work on the computation of a structured low rank approximation of the Sylvester resultant matrix of two inexact polynomials and . Specifically, it has been shown in previous work that these polynomials must be processed before a structured low rank approximation of is computed. The existing algorithm may still, however, yield a structured low rank approximation of , but not a structured low rank approximation of , which is unsatisfactory. Moreover, a structured low rank approximation of must be equal to, apart from permutations of its columns, a structured low rank approximation of , but the existing algorithm does not guarantee the satisfaction of this condition. This paper addresses these issues by modifying the existing algorithm, such that these deficiencies are overcome. Examples that illustrate these improvements are shown. [Copyright &y& Elsevier]

Abstract: Given a Probabilistic Boolean Network (PBN), an important problem is to study its steady-state probability distribution for network analysis. In this paper, we present a new perturbation bound of the steady-state probability distribution of PBNs with gene perturbation. The main contribution of our results is that this new bound is established without additional condition required by the existing method. The other contribution of this paper is to propose a fast algorithm based on the special structure of a transition probability matrix of PBNs with gene perturbation to compute its steady-state probability distribution. Experimental results are given to demonstrate the effectiveness of the new bound, and the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper considers structured matrix methods for the calculation of the theoretically exact roots of a polynomial whose coefficients are corrupted by noise, and whose exact form contains multiple roots. The addition of noise to the exact coefficients causes the multiple roots of the exact form of the polynomial to break up into simple roots, but the algorithms presented in this paper preserve the multiplicities of the roots. In particular, even though the given polynomial is corrupted by noise, and all computations are performed on these inexact coefficients, the algorithms ‘sew’ together the simple roots that originate from the same multiple root, thereby preserving the multiplicities of the roots of the theoretically exact form of the polynomial. The algorithms described in this paper do not require that the noise level imposed on the coefficients be known, and all parameters are calculated from the given inexact coefficients. Examples that demonstrate the theory are presented. [Copyright &y& Elsevier]

Abstract: This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) . We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis. [Copyright &y& Elsevier]

Abstract: Over the last years, various fast algorithms for computing the determinant of a pentadiagonal Toeplitz matrices were developed. In this paper, we give a new kind of elementary algorithm requiring operations, where is an integer that needs to be chosen freely at the beginning of the algorithm. For example, we can compute in and operations if we choose as and , respectively. For various applications, it will be enough to test if the determinant of a pentadiagonal Toeplitz matrix is zero or not. As in another result of this paper, we used modular arithmetic to give a fast algorithm determining when determinants of such matrices are non-zero. This second algorithm works only for Toeplitz matrices with rational entries. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to gain more insight into vector and matrix medians and to investigate algorithms to compute them. We prove relations between vector and matrix means and medians, particularly regarding the classical structure tensor. Moreover, we examine matrix medians corresponding to different unitarily invariant matrix norms for the case of symmetric 2×2 matrices, which frequently arise in image processing. Our findings are explained and illustrated by numerical examples. To solve the corresponding minimization problems, we propose several algorithms. Existing approaches include Weiszfeld’s algorithm for the computation of vector medians and semi-definite programming, in particular, second order cone programming, which has been used for matrix median computation. In this paper, we adapt Weiszfeld’s algorithm for our setting and show that also two splitting methods, namely the alternating direction method of multipliers and the parallel proximal algorithm, can be applied for generalized vector and matrix median computations. Besides, we compare the performance of these algorithms numerically and apply them within local median filters. [Copyright &y& Elsevier]

Abstract: The linear complementarity problem is to find a vector in satisfying , ,, where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems. [Copyright &y& Elsevier]

Abstract The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite or indefinite proximal term and updates the Lagrangian multiplier twice in different ways. Furthermore, the proposed G-LADMM can be expressed as a proximal point algorithm (PPA), and all the subproblems are just to estimate the proximity operator of the function in the objective. We specify the domain of the proximal parameter and stepsizes to guarantee that G-LADMM is globally convergent. It turns out that our convergence domain of the proximal parameter and stepsizes is significantly larger than other convergence domains in the literature. The numerical experiments illustrate the improvements of the proposed G-LADMM to solve LASSO and image decomposition problems. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present an inverse iteration algorithm, to find the H-spectral radius and the associated positive eigenvector of a nonnegative weakly irreducible tensor, which always preserve the positivity of approximate eigenvectors. The local quadratical convergence of the proposed algorithm is established based on a basic result of the Newton's method for solving nonlinear equations. Some numerical examples illustrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract It is known, that proper parameterizations of rational curves in reduced form are unique up to bilinear reparameterizations, i.e., projective transformations of its parameter domain. This observation has been used in a series of papers by Alcázar et al. to formulate algorithms for detecting Euclidean equivalences and symmetries as well as similarities. We generalize this approach to projective equivalences of rationally parametrized surfaces. More precisely, we observe that a birational base-point free parameterization of a surface is unique up to projective transformations of the domain. Furthermore, we use this insight to find all projective equivalences between two given surfaces. In particular, we formulate a polynomial system of equations whose solutions specify the projective equivalences, i.e., the reparameterizations associated with them. Furthermore, we investigate how this system simplifies for the special case of affine equivalences for polynomial surfaces and how we can use our method to detect projective symmetries of surfaces. This method can be used for classifying the generic cases of quadratic surfaces. [ABSTRACT FROM AUTHOR]

Abstract In the present paper, we devote our effort to solve a nonlinear inverse problem for identifying a time-dependent convection coefficient in a time-fractional diffusion equation from the measured data at an interior point for one-dimensional case. We prove the existence, uniqueness and regularity of solution for the direct problem by using the fixed point theorem. The stability of inverse convection coefficient problem is obtained based on the regularity of solution for the direct problem and some generalized Gronwall's inequalities. We use a modified optimal perturbation regularization algorithm to solve the inverse convection coefficient problem. Two numerical examples are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show that it is possible to estimate the backward error for the approximation of the matrix exponential on-the-fly , without the need to precompute in high precision quantities related to specific accuracies. In this way, the scaling parameter s and the degree m of the truncated Taylor series (the underlying method) are adapted to the input matrix and not to a class of matrices sharing some spectral properties, such as with the classical backward error analysis. The result is a very flexible method which can approximate the matrix exponential at any desired accuracy. Moreover, the risk of overscaling, that is the possibility to select a value s larger than necessary, is mitigated by a new choice as the sum of two powers of two. Finally, several numerical experiments in MATLAB with data in double and variable precision and with different tolerances confirm that the method is accurate and often faster than available good alternatives. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes the Lanczos type of biconjugate residual (BCR) algorithm for solving the quadratic inverse eigenvalue problem L 2 X Λ 2 + L 1 X Λ + L 0 X = 0 where L 2 , L 1 and L 0 should be partially bisymmetric under a prescribed submatrix constraint. An analysis reveals that the algorithm obtains the solutions of the constrained quadratic inverse eigenvalue problem in finitely many steps in the absence of round-off errors. Finally numerical results are performed to confirm the analysis and to illustrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the constructing methods of a recombined multinomial tree based on saddle-point approximation and its application to Levy models options pricing. Firstly, the Levy process and the European option pricing are introduced. Then, we used the characteristic function of Levy process to generate density function value at discrete point in a certain range, based on the saddle-point approximation method. Then, we provide the method to construct recombined multinomial tree and give the pricing formula of European option and path-dependent option pricing based on the backward iteration. Finally, we used the CGMY process to demonstrate its application to European option, American option and American barrier option pricing. It proves that saddle-point approximation turns the inverse Fourier integral transform problem to several function value calculation. Comparing to IFFT, the speed of calculation using this method is faster, and it avoid the negative probability density function value based on IFFT. Because of the linear growth of the number of nodes, we can extend the saddle-point approximation method to the calculation of path-dependent option. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, and a dimensional reduction procedure to identify important modes of the solution. We next develop and analyze an a posteriori error indicator, and the corresponding adaptive algorithm. In addition, we will construct a coupled offline–online adaptive algorithm, which provides an adaptive strategy to the selection of offline and online basis functions. Our theory shows that the convergence is robust with respect to the heterogeneities and contrast of the media. We present several numerical results to illustrate the performance of our method. [ABSTRACT FROM AUTHOR]

Abstract A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues to solve from the industrial viewpoint of these new devices. The statistical features of variability have been usually studied making use of Weibull distribution. However, this probability distribution does not work correctly for some resistive memories, in particular for those based on the Ni/HfO 2 /Si structure that has been employed in this work. A completely new approach based on phase-type modeling is proposed in this paper to characterize the randomness of resistive memories operation. An in-depth comparison with experimental results shows that the fitted phase-type distribution works better than the Weibull distribution and also helps to understand the physics of the resistive memories. Highlights • Reliability analysis of switching parameters in Resistive Random Access Memories (RRAMS) is developed. • The lack of fit of the Weibull model is shown with data of voltage up to the conductive filament failure (Vreset). • A new statistical modeling of Vreset based on phase-type distributions (PHDs) is introduced. • Estimation and selection of parameters of the PHD via EM algorithm provide the Erlang distribution (ED) as the best fit. • The ED has two parameters with a clear physical interpretation. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a two-level MacCormack rapid solver method for solving a 2D time dependent Navier–Stokes problem that models an incompressible fluid flow. A decoupling approach based on the coupling term via spatial extrapolation is proposed for devising decoupled marching algorithms for the nonstationary incompressible model. In this hybrid method, an explicit MacCormack scheme provides a H 1 -optimal velocity approximation and a L 2 -optimal pressure approximation by solving a nonlinear Navier–Stokes problem on a coarse grid with mesh size H , while an implicit Crank–Nicolson algorithm consists in dealing with the fully discrete linear generalized Stokes problem on a fine grid with mesh size h ≪ H. The theoretical result suggests that our method is unconditionally stable over long time intervals. While the numerical evidences both confirm the theoretic analysis and show that the algorithm is convergent, the tests also suggest that our method is both cheaper and faster than the two-level finite element Galerkin scheme. [ABSTRACT FROM AUTHOR]

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: This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch. [Copyright &y& Elsevier]

Abstract: This work studies an inverse problem of determining the first-order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point. Being different from other ordinary parameter identification problems in parabolic equations, in our mathematical model there exists degeneracy on the lateral boundaries of the domain, which may cause the corresponding boundary conditions to go missing. By the contraction mapping principle, the uniqueness of the solution for the inverse problem is proved. A numerical algorithm on the basis of the predictor–corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown function is recovered very well. The results obtained in the paper are interesting and useful, and can be extended to other more general inverse coefficient problems of degenerate PDEs. [Copyright &y& Elsevier]

Abstract: In this paper, we study the following minimization problem where is a bounded linear operator, is some constant, is a potential function for , is the set of fixed points of nonexpansive mapping and is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem. [Copyright &y& Elsevier]

Abstract: Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Padé approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper is about the construction of univariate wavelet bi-frames with each framelet being symmetric. As bivariate filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms have high symmetry so that it is possible to design the corresponding multiresolution algorithms for extraordinary vertices. For open surfaces, special multiresolution algorithms are designed to process boundary vertices. When the multiresolution algorithms derived from univariate wavelet bi-frames are used as the boundary algorithms, it is desired that not only the scaling functions but also all framelets be symmetric. In addition, the algorithms for curve/surface multiresolution processing should be given by templates so that they can be easily implemented. In this paper, first, by appropriately associating the lowpass and highpass outputs to the nodes of , we show that both biorthogonal wavelet multiresolution algorithms and bi-frame multiresolution algorithms can be represented by templates. Then, using the idea of the lifting scheme, we provide frame algorithms given by several iterative steps with each step represented by a symmetric template. Finally, with the given templates of algorithms, we obtain the corresponding filter banks and construct bi-frames based on their smoothness and vanishing moments. Two types of symmetric bi-frames are studied in this paper. In order to provide a clearer picture on the template-based procedure for bi-frame construction, in this paper we also consider the template-based construction of biorthogonal wavelets. The approach of the template-based bi-frame construction introduced in this paper can be extended easily to the construction of bivariate bi-frames with high symmetry for surface multiresolution processing. [ABSTRACT FROM AUTHOR]

Abstract: In the past decades, fuzzy segmentation methods, especially the fuzzy -means algorithms, have been widely used in the segmentation of brain medical images, because they can preserve more information from the original image than other segmentation methods. This paper introduces a modified robust fuzzy -means algorithm with special weighted bias estimation for segmentation of brain magnetic resonance image. In general, the intensity inhomogeneities are endorsed to imperfections in the radio-frequency coils or to the problems connected with the image acquisition. The intensity inhomogeneities are seriously affecting the segmentation process when computer assisted segmentation algorithms used in differentiating borders between the tissues in medical images. The proposed algorithm of this paper is considered the fact in the standard fuzzy -means with no spatial context information, which makes it sensitive to noise. Hence the proposed method is capable to deal with the intensity inhomogeneities and noised image effectively. Further, to reduce the number of iterations, the proposed modified robust algorithm initializes the centroid using dist-max initialization algorithm before the execution of algorithm iteratively. Experimental results carried out through the comparative studies of segmentation results of the proposed method and the segmentation results of other existed algorithms when these algorithms implemented on brain magnetic resonance image and benchmark lung cancer dataset. The superiority of the proposed method has shown from the experimental results. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective. [ABSTRACT FROM AUTHOR]

In this paper, we propose a norm descent derivative-free algorithm for solving large-scale nonlinear symmetric equations without involving any information of the gradient or Jacobian matrix by using some approximate substitutions. The proposed algorithm is extended from an efficient three-term conjugate gradient method for solving unconstrained optimization problems, and inherits some nice properties such as simple structure, low storage requirements and symmetric property. Under some appropriate conditions, the global convergence is proved. Finally, the numerical experiments and comparisons show that the proposed algorithm is very effective for large-scale problems. [ABSTRACT FROM AUTHOR]

The present paper proposes a new approach to the classical problem of the harmonic oscillations of a thin wing in a flow of non-viscous incompressible fluid. The problem is reduced to a dual integral equation, permitting application of numerical methods. The numerical experiments are performed by using some advanced fast non-stationary iterative methods, with the help of the two-dimensional Fast Fourier Transform. There is given a brief survey on the iterative methods, to evaluate the most efficient algorithms in application to the considered problem of the flapping wing theory. [ABSTRACT FROM AUTHOR]