• Numer. Algor. (IF 2.064) Pub Date : 2020-09-23
Marzieh Hasannasab, Johannes Hertrich, Friederike Laus, Gabriele Steidl

In this paper, we consider maximum likelihood estimations of the degree of freedom parameter ν, the location parameter μ and the scatter matrix Σ of the multivariate Student t distribution. In particular, we are interested in estimating the degree of freedom parameter ν that determines the tails of the corresponding probability density function and was rarely considered in detail in the literature

更新日期：2020-09-23
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-22
Xueli Bai, Hongjin He, Chen Ling, Guanglu Zhou

This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular $${\mathscr{M}}$$-tensor and a nonnegative right-hand side vector, it may have multiple nonnegative solutions. In this paper, we propose an algorithm which can always preserve

更新日期：2020-09-22
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-21
Amparo Gil, Javier Segura, Nico M. Temme

Iterative methods with certified convergence for the computation of Gauss–Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be generally faster than previous methods and without practical restrictions on the range of the parameters. The evaluation of the nodes and weights of the quadrature is exclusively

更新日期：2020-09-21
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-14
S. Nemati, Pedro M. Lima, Delfim F. M. Torres

We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss–Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is first transformed into the interval [− 1, 1], by considering a suitable change of variable. Then, by introducing special Jacobi parameters, the integral part is approximated

更新日期：2020-09-14
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-12
D.R. Sahu, Y.J. Cho, Q.L. Dong, M.R. Kashyap, X.H. Li

The split feasibility problem is to find a point x∗ with the property that x∗∈ C and Ax∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y, respectively, and A is a bounded linear operator from X to Y. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce

更新日期：2020-09-13
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-12
Fátima Lizarte, Teresa E. Pérez, Miguel A. Piñar

In this work, a Sobolev inner product on the unit ball of $$\mathbb {R}^{d}$$ involving the outward normal derivative is considered. A basis of mutually orthogonal polynomials associated with this inner product is constructed in terms of spherical harmonics and a radial part obtained from a family of univariate polynomials orthogonal with respect to a Sobolev inner product. The properties of this family

更新日期：2020-09-12
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-11
Fan Yang, Qu Pu, Xiao-Xiao Li

This paper is devoted to solve an inverse problem for identifying the source term of a time-fractional nonhomogeneous diffusion equation with a fractional Laplacian in a non-local boundary. Based on the expression of the solution for the direct problem, the inverse problem for searching the space source term is converted into solving the first kind of Fredholm integral equation. The conditional stability

更新日期：2020-09-12
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-09
Haoen Huang, Dongyang Fu, Guancheng Wang, Long Jin, Shan Liao, Huan Wang

The solution of nonlinear optimization is usually encountered in many fields of scientific researches and engineering applications, which spawns a large number of corresponding algorithms to cope with it. Besides, with developments of modern cybernetics technology, it imperatively requires some advanced numerical algorithms to solve online dynamic nonlinear optimization (ODNO). Nevertheless, the major

更新日期：2020-09-10
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-09
Lakhdar Elbouyahyaoui, Mohammed Heyouni, Azita Tajaddini, Farid Saberi-Movahed

The problem of shifted linear systems is an important and challenging issue in a number of research applications. Krylov subspace methods are effective techniques for different kinds of this problem due to their advantages in large and sparse matrix problems. In this paper, two new block projection methods based on respectively block FOM and block GMRES are introduced for solving sequences of shifted

更新日期：2020-09-10
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-07
Tong Zhang, Mengmeng Duan

In this paper, we consider the Galerkin finite element method (FEM) for the Kelvin-Voigt viscoelastic fluid flow model with the lowest equal-order pairs. In order to overcome the restriction of the so-called inf-sup conditions, a pressure projection method based on the differences of two local Gauss integrations is introduced. Under some suitable assumptions on the initial data and forcing function

更新日期：2020-09-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-07
Qun Li, Bing Zheng

In this paper, two effective derivative-free methods are proposed for solving large-scale nonlinear monotone equations, in which the search directions are sufficiently descent and independent of the line search. The methods are the extensions of the conjugate gradient methods proposed by Bojari and Eslahchi (Numer. Algorithms 83, pp. 901–933, 2020) combined with the hyperplane projection technique

更新日期：2020-09-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-07
Alessandro Buccini, Mirjeta Pasha, Lothar Reichel

Bregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality of the computed solutions they deliver. However, these iterative methods may require a large number of iterations and this reduces their usefulness. This paper develops a computationally attractive linearized Bregman algorithm by projecting the problem to be solved

更新日期：2020-09-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-04

In our work, we consider the linear least squares problem for m × n-systems of linear equations Ax = b, m ≥ n, such that the matrix A and right-hand side vector b can vary within an interval m × n-matrix A and an interval m-vector b, respectively. We have to compute, with a prescribed accuracy, outer coordinate-wise estimates of the set of all least squares solutions to Ax = b for A ∈A and b ∈b. Our

更新日期：2020-09-05
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-04
Xindong Liu, Zili Chen, Jinxing Liu

The purpose of this paper is to propose an algorithm for solving the split common fixed point problem for strict quasi-ϕ-pseudocontractive mappings in Banach spaces. It is proved that the sequence generated by the proposed iterative algorithm converges strongly to a solution of the split common fixed point problem. Then, the main result is used to study the split common null point problem and the split

更新日期：2020-09-05
• Numer. Algor. (IF 2.064) Pub Date : 2020-09-03
Munish Kansal, Alicia Cordero, Sonia Bhalla, Juan R. Torregrosa

In this paper, a two-step class of fourth-order iterative methods for solving systems of nonlinear equations is presented. We further extend the two-step class to establish a new sixth-order family which requires only one additional functional evaluation. The convergence analysis of the proposed classes is provided under several mild conditions. A complete dynamical analysis is made, by using real

更新日期：2020-09-03
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-31

The k th Fréchet derivative of a matrix function f is a multilinear operator from a cartesian product of k subsets of the space $$\mathbb {C}^{n\times n}$$ into itself. We show that the k th Fréchet derivative of a real-valued matrix function f at a real matrix A in real direction matrices E1, E2, $$\dots$$, Ek can be computed using the complex step approximation. We exploit the algorithm of Higham

更新日期：2020-08-31
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-31
Chengjian Zhang, Xiaoqiang Yan

Delay-differential-algebraic equations have been widely used to model some important phenomena in science and engineering. Since, in general, such equations do not admit a closed-form solution, it is necessary to solve them numerically by introducing suitable integrators. The present paper extends the class of block boundary value methods (BBVMs) to approximate the solutions of nonlinear delay-differential

更新日期：2020-08-31
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-30
L. Gr. Ixaru

We show that a direct numerical computation of the coefficients of any method based on the exponential fitting is possible. This makes unnecessary the knowledge of long sets of analytical expressions for the coefficients, as usually presented in the literature. Consequently, the task of any potential user for writing his/her own code becomes much simpler. The approach is illustrated on the case of

更新日期：2020-08-30
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-30
Harry Oviedo, Oscar Dalmau, Hugo Lara

This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction. These iterative algorithms use a projection operator based on the QR factorization to preserve

更新日期：2020-08-30
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-29
Filip Chudy, Paweł Woźny

Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis, and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of these polynomials and their linear combinations. New simple recurrence relations of low order satisfied by dual Bernstein polynomials are given. In particular,

更新日期：2020-08-29
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-27
Carla Jesus, Ercília Sousa

Lévy flights are generalised random walk processes where the independent stationary increments are drawn from a long-tailed α-stable jump length distribution. We consider the formulation of Lévy flights, for 0 < α < 1, in terms of a space-fractional diffusion equation which fundamental solutions are the probability density functions. First, we present how to obtain the governing equation of Lévy motion

更新日期：2020-08-27
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-27
Xu Chen, Deng Ding, Siu-Long Lei, Wenfei Wang

Recently, fractional partial differential equations have been widely applied in option pricing problems, which better explains many important empirical facts of financial markets, but rare paper considers the multi-state options pricing problem based on fractional diffusion models. Thus, multi-state European option pricing problem under regime-switching tempered fractional partial differential equation

更新日期：2020-08-27
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-25
Andrea Raffo, Silvia Biasotti

Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds, we propose the weighted quasi-interpolant spline approximation method (wQISA). We provide global and local bounds of the method and discuss how it still preserves the

更新日期：2020-08-25
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-20
Igor Omelyan, Yuri Kozitsky, Krzysztof Pilorz

An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in $$\mathbb {R}^{d} (d \geq 1)$$. The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically

更新日期：2020-08-20
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-19
Guoyu Zhang, Chengming Huang, Mingfa Fei, Nan Wang

In this paper, we propose a linearized finite element method for solving two-dimensional fractional Klein-Gordon equations with a cubic nonlinear term. The employed time discretization is a weighted combination of the L2 − 1σ formula introduced recently by Lyu and Vong (Numer. Algorithms 78(2):485–511, 2018), Galerkin finite element method is used for the spatial discretization, and the cubic nonlinear

更新日期：2020-08-19
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-18
Long Yuan

In this paper, we first consider the time-harmonic Maxwell equations with Dirichlet boundary conditions in three-dimensional anisotropic media, where the coefficients of the equations are general symmetric positive definite matrices. By using scaling transformations and coordinate transformations, we build the desired stability estimates between the original electric field and the transformed nonphysical

更新日期：2020-08-18
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-14
Kamal Shanazari, Siamak Banei

We present a truly meshless method based on the thin plate splines for the numerical solution of the two dimensional forward-backward heat equation and give a robust formulation for the proposed method. The physical domain is divided into two subdomains each of which defines a forward or a backward subproblem. The resulting subproblems are treated by a radial basis function method for spatial dimension

更新日期：2020-08-14
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-12
Longfei Ren, Chengjing Wang, Peipei Tang, Zheng Ma

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation (TV) has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels. However, the computation task for hyperspectral

更新日期：2020-08-12
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-08
Avinash Malik

Stochastic hybrid systems (SHSs) are a modelling framework for a cyber-physical system (CPS), used to simulate, validate, and verify safety critical controllers under uncertainty. Popular simulation tools can miss detecting discontinuities when simulating SHS, thereby producing incorrect outputs during simulation. We propose a novel adaptive step size simulation/integration technique for a subset of

更新日期：2020-08-09
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-08
X. Antoine, E. Lorin, Y. Zhang

This paper is devoted to the derivation and analysis of accurate and efficient perfectly matched layers (PMLs) or efficient absorbing layers for solving fractional Laplacian equations within initial boundary value problems (IBVP). Two main approaches are derived: we first propose a Fourier-based pseudospectral method, and then present a real space method based on an efficient computation of the fractional

更新日期：2020-08-09
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-08
Fu-Rong Lin, Qiu-Ya Wang, Xiao-Qing Jin

In this paper, high-order finite difference methods are proposed to solve the initial-boundary value problem for space Riesz variable-order fractional diffusion equations. Based on weighted-shifted-Grünwald-difference (WSGD) operators proposed in Lin and Liu (J. Comput. Appl. Math. 363, 77–91 (2020)) for Riemann-Liouville fractional derivatives, we derive WSGD operators for variable-order ones by using

更新日期：2020-08-09
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-07
Zhao Yang, Rong Huang, Wei Zhu, Jianzhou Liu

In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accurately solved with an “ideal” componentwise forward error. In particular, a pleasantly small componentwise

更新日期：2020-08-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-07
Jinzhi Huang, Zhongxiao Jia

For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair (A,B) of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a generalized eigensolver can be applied to one of them and the desired GSVD components are then recovered from the computed generalized eigenpairs. Our concern in this paper

更新日期：2020-08-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-06
Geovani N. Grapiglia, Ekkehard W. Sachs

We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative parameters. We obtain complexity bounds to achieve approximate first-order optimality even when this sequence is not summable.

更新日期：2020-08-08
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-03
R. Dehghani, N. Bidabadi, M. M. Hosseini

In order to get a higher order accuracy of approximating the Hessian matrix of the objective function, we use the chain rule and propose two modified secant equations. An interesting property of the proposed methods is that these utilize information from two most recent steps where the usual secant equation uses only the latest step information. The other point of interest to one of the proposed methods

更新日期：2020-08-03
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-01
Roger Behling, Yunier Bello-Cruz, Luiz-Rafael Santos

The ancient concept of circumcenter has recently given birth to the circumcentered-reflection method (CRM). CRM was first employed to solve best approximation problems involving affine subspaces. In this setting, it was shown to outperform the most prestigious projection-based schemes, namely, the Douglas-Rachford method (DRM) and the method of alternating projections (MAP). We now prove convergence

更新日期：2020-08-01
• Numer. Algor. (IF 2.064) Pub Date : 2020-08-01
Fang Chen, Tian-Yi Li

For the discrete linear system resulted from the considered steady-state space-fractional diffusion equations, we propose an improved scaled HSS (ISHSS) iteration method and discuss its convergence theory. Then, we construct a fast ISHSS (FISHSS) preconditioner to accelerate the convergence rates of the Krylov subspace iteration methods. We discuss the spectral properties of the FISHSS preconditioning

更新日期：2020-08-01
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-30
Zhengguang Liu

The Swift-Hohenberg model is a very important phase field crystal model which can be described many crystal phenomena. This model with quadratic-cubic nonlinearity based on the H− 1-gradient flow approach is a sixth-order system which satisfies mass conservation and energy dissipation law. The negative energy of this model will bring huge difficulties to energy stability for many existing approaches

更新日期：2020-07-30
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-29
Peng Wang, Yanzhao Cao, Xiaoying Han, Peter Kloeden

The aim of this work is to analyze the mean-square convergence rates of numerical schemes for random ordinary differential equations (RODEs). First, a relation between the global and local mean-square convergence order of one-step explicit approximations is established. Then, the global mean-square convergence rates are investigated for RODE-Taylor schemes for general RODEs, Affine-RODE-Taylor schemes

更新日期：2020-07-29
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-27
Simeon Reich, Duong Viet Thong, Qiao-Li Dong, Xiao-Huan Li, Vu Tien Dung

We propose and study new projection-type algorithms for solving pseudomonotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of the cost operators. We prove weak and strong convergence theorems for the sequences generated by these new methods. The numerical behavior of the proposed algorithms when applied to several test problems is compared with that

更新日期：2020-07-27
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-23
T. E. Simos, Ch. Tsitouras

Two new Runge–Kutta (RK) pairs of orders 6(4) and 7(5) are presented for solving numerically the inhomogeneous linear initial value problems with constant coefficients. These new pairs use only six and eight stages per step respectively. Six stages are needed for conventional Runge–Kutta pairs of orders 5(4) while for such a pair of orders 6(5) we use eight stages. Thus, our proposal is an improvement

更新日期：2020-07-23
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-23
Pin Lyu, Seakweng Vong

In this paper, we study a fast linearized numerical method for solving nonlinear time-fractional diffusion equations. A new weighted method is proposed to construct linearized approximation, which enables the unconditional convergence to be established when the nonlinearity f(u) is only locally Lipschitz continuous. In order to reduce the computational cost, the sum-of-exponentials (SOE) technique

更新日期：2020-07-23
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-22
Jianfeng Luo, Xiaozhou Wang, Yi Zhao

In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the

更新日期：2020-07-22
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-21
Stefan Kunis, Dominik Nagel

We prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are “off the grid,” pairs of nodes nearly collide, and the studied condition number grows linearly with the inverse separation distance. Such growth rates are known in greater generality if all nodes collide or for groups of colliding nodes. For pairs

更新日期：2020-07-21
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-21
Bengt Fornberg

In computational contexts, analytic functions are often best represented by grid-based function values in the complex plane. For integrating periodic functions, the spectrally accurate trapezoidal rule (TR) then becomes a natural choice, due to both accuracy and simplicity. The two key present observations are (i) the accuracy of TR in the periodic case can be greatly increased (doubling or tripling

更新日期：2020-07-21
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-20
Mahboub Baccouch

This paper is concerned with the convergence and superconvergence of the local discontinuous Galerkin (LDG) finite element method for nonlinear fourth-order boundary value problems of the type $$u^{(4)}=f(x,u,u^{\prime },u^{\prime \prime },u^{\prime \prime \prime })$$, x ∈ [a,b] with classical boundary conditions at the endpoints. Convergence properties for the solution and for all three auxiliary

更新日期：2020-07-20
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-18
Shan-Mou Cao, Zeng-Qi Wang

The preconditioned modified Hermitian/skew-Hermitian splitting (PMHSS) iteration method and the corresponding preconditioning technique can achieve satisfactory results for solving optimal control problems governed by Poisson’s equation. We explore the feasibility of such a method and preconditioner for solving optimization problems constrained by the more complicated Stokes system. Theoretical results

更新日期：2020-07-18
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-15
Bosu Choi, Andrew Christlieb, Yang Wang

In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In 11Adaptive Sublinear Time Fourier Algorithm” by Lawlor et al. (Adv. Adapt. Data Anal.5(01):1350003, 2013), an efficient algorithm with $${\Theta }(k\log k)$$ average-case runtime and Θ(k) average-case sampling complexity for the one-dimensional sparse FFT was developed for signals of bandwidth

更新日期：2020-07-15
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-12
Xue-Feng Duan, Juan Li, Shan-Qi Duan, Qing-Wen Wang

In this paper, we consider the generalized nonnegative tensor factorization (GNTF) problem, which arises in multiple-tissue gene expression and multi-target tracking. Based on the Karhsh-Kuhn-Tucker conditions, the necessary condition of the local solution for the GNTF problem is given. The proximal alternating nonnegative least squares method is designed to solve it, and its convergence theorem is

更新日期：2020-07-13
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-11
Xing Huang, Fen-Fen Yang

In this paper, the existence and uniqueness of the distribution-dependent SDEs with the Hölder continuous drift driven by a α-stable process are investigated. Moreover, by using the Zvonkin-type transformation, the convergence rate of the Euler–Maruyama method and propagation of chaos is also obtained. The results cover the ones in the case of distribution-independent SDEs.

更新日期：2020-07-13
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-11
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang

The circumcentered Douglas–Rachford method (C–DRM), introduced by Behling, Bello Cruz and Santos, iterates by taking the circumcenter of associated successive reflections. It is an acceleration of the well-known Douglas-Rachford method (DRM) for finding the best approximation onto the intersection of finitely many affine subspaces. Inspired by the C–DRM, we introduced the more flexible circumcentered

更新日期：2020-07-13
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-10
Yunong Zhang, Xiao Liu, Yihong Ling, Min Yang, Huanchang Huang

Zeroing dynamics (ZD) has shown great performance to solve various time-varying problems. In this paper, the problem of time-varying Sylvester-transpose matrix inequality is first investigated. Since it is difficult to solve a matrix inequality with a matrix variable and its transpose by traditional methods, this paper proposes a continuous ZD (CZD) model by employing ZD design formula and JMP function

更新日期：2020-07-10
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-10
Toni Karvonen, Simo Särkkä, Ken’ichiro Tanaka

We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel interpolants at the resulting points. If the kernel is Gaussian, we show that the approximate Fekete points in one dimension are the solution to a convex optimisation

更新日期：2020-07-10
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-04
Pham Ngoc Anh, T. V. Thang, H. T. C. Thach

In this paper, we introduce new approximate projection and proximal algorithms for solving multivalued variational inequalities involving pseudomonotone and Lipschitz continuous multivalued cost mappings in a real Hilbert space. The first proposed algorithm combines the approximate projection method with the Halpern iteration technique. The second one is an extension of the Halpern projection method

更新日期：2020-07-05
• Numer. Algor. (IF 2.064) Pub Date : 2020-07-03
Yingzhi Liu, Xiao-Chuan Cai

We consider numerical simulation of blood flows in the artery using multilevel domain decomposition methods. Because of the complex geometry, the construction and the solve of the coarse problem take a large percentage of the total compute time in the multilevel method. In this paper, we introduce a one-dimensional central-line model of the blood flow and use its stabilized finite element discretization

更新日期：2020-07-03
• Numer. Algor. (IF 2.064) Pub Date : 2020-06-29
Raffaele D’Ambrosio, Carmela Scalone

The paper is focused on analyzing the conservation issues of stochastic 𝜃-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its discretization through stochastic 𝜃-methods, by preserving the correlation matrix. This evidence is equivalent to accurately maintaining the stationary

更新日期：2020-07-02
• Numer. Algor. (IF 2.064) Pub Date : 2020-06-29
R. M. Asharabi, J. Prestin

The bivariate sinc-Gauss sampling formula is introduced in Asharabi and Prestin (IMA J. Numer. Anal. 36:851–871, 2016) to approximate analytic functions of two variables which satisfy certain growth condition. In this paper, we apply this formula to approximate partial derivatives of any order for entire and holomorphic functions on an infinite horizontal strip domain using only finitely many samples

更新日期：2020-07-01
• Numer. Algor. (IF 2.064) Pub Date : 2020-06-26
J. M. Carnicer, E. Mainar, J. M. Peña

Disk polynomials form a basis of orthogonal polynomials on the disk corresponding to the radial weight $${\alpha +1 \over \pi }(1-r^{2})^{\alpha }$$. In this paper, the stability properties of disk polynomials are analyzed. A conditioning associated with the representation of the least squares approximation with respect to this basis is introduced and bounded. Among all disk polynomials, the least

更新日期：2020-06-26
• Numer. Algor. (IF 2.064) Pub Date : 2020-06-21
Thái Anh Nhan, Relja Vulanović

A linear two-dimensional singularly perturbed convection-diffusion boundary-value problem is considered. The problem is discretized by the upwind finite-difference method. The analysis of this method on Shishkin-type meshes has been well-established, but the discretization mesh in this paper is the original Bakhvalov mesh, introduced in 1969 as the first layer-adapted mesh. We analyze the error of

更新日期：2020-06-22
• Numer. Algor. (IF 2.064) Pub Date : 2020-06-18
A. Kouibia, M. Pasadas, R. Akhrif

In this paper, we propose a variational method in order to solve Bratu’s problem for two dimensions in an adequate space of biquadratic spline functions. The solution is obtained by resolving a sequence of boundary value problems. We study some characterizations of the functions of such sequence and we express them as some linear combination of biquadratic spline bases functions. We finish by showing

更新日期：2020-06-18
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