查看更多>>摘要：We introduce a new concept of convergence for iterative methods, named restricted global convergence, that consists of locating a solution and obtaining a domain of global convergence. As a consequence, results of semilocal convergence and local convergence are obtained. For this, we use auxiliary points and obtain balls of convergence. The study is illustrated with Chebyshev's method. (C) 2020 Elsevier B.V. All rights reserved.
Kumar, KamaleshChakravarthy, P. PramodRamos, HiginioVigo-Aguiar, Jesus...
15页
查看更多>>摘要：This article presents a stable finite difference approach for the numerical approximation of singularly perturbed differential-difference equations (SPDDEs). The proposed scheme is oscillation-free and much accurate than conventional methods on a uniform mesh. Error estimates show that the scheme is linear convergent in space and time variables. By using the Richardson extrapolation technique, the obtained results are extrapolated in order to get better approximations. Some numerical examples are taken from literature to validate the theory, showing good performance of the proposed method. (c) 2020 Published by Elsevier B.V.
查看更多>>摘要：Regularization is possibly the most popular method for solving discrete ill-posed prob-lems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for large Tikhonov regularization in standard form. The proposed TR-MTRSVD algorithm introduces the idea of randomized algorithm into the improved truncated singular value decomposition (MTSVD) method to solve large Tikhonov regularization problems. The approximation matrix A & SIM;l produced by randomized SVD is replaced by the closest matrix A & SIM;k & SIM; in a unitarily invariant matrix norm with the same spectral condition number. The regularization parameters are determined by the discrepancy principle. Numerical examples show the effectiveness and efficiency of the proposed TR-MTRSVD algorithm for large Tikhonov regularization problems. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Many conservative systems in physical sciences can be described by multi-symplectic Hamiltonian PDEs (MS-HPDEs) admitting three important inherent properties named as multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we develop a novel strategy to systematically derive linearly implicit local energy-preserving schemes for general MS-HPDEs, which is named the exponential invariant energy quadratization approach (EIEQ). Such novel strategy is based on the exponential form of non-quadratic terms of the state function that can remove the bounded-from-below restriction, so it is more applicable than the traditional IEQ approach widely employed to construct linearly implicit schemes. Moreover, we provide a completely explicit discretization of the auxiliary variable combined with the nonlinear term, which obtains linearly implicit schemes of the constant coefficient, making their more effective than the IEQ schemes for rapid simulations. We also present the multiple EIEQ approach to improve the applicability of the EIEQ approach for MS-HPDEs with more non-quadratic terms. In addition, when periodic or homogeneous boundary conditions are considered, the proposed schemes are global energy-preserving and can be explicitly solved by using the fast Fourier transform. Finally, ample numerical tests are carried out to demonstrate the computational efficiency, conservation and accuracy of EIEQ schemes. (c) 2021 Elsevier B.V. All rights reserved.
Aledo, Juan A.Diaz, Luis G.Martinez, SilviaValverde, Jose C....
14页
查看更多>>摘要：It is well known that periodic orbits with any period can appear in sequential dynamical systems over undirected graphs with a Boolean maxterm or minterm function as global evolution operator. Indeed, fixed points cannot coexist with periodic orbits of greater periods, while periodic orbits with different periods greater than 1 can coexist. Additionally, a fixed point theorem about the uniqueness of a fixed point is known. In this paper, we provide an m-periodic orbit theorem (for m > 1) and we give an upper bound for the number of fixed points and periodic orbits of period greater than 1, so completing the study of the periodic structure of such systems. We also demonstrate that these bounds are the best possible ones by providing examples where they are attained. (c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we consider some preconditioning techniques for a class of block three-by three saddle point problems, which arise from a coupled diffuse element-finite element technique for transient coupled-field analysis and some other applications. Firstly, we propose an exact parameterized block symmetric positive definite preconditioner for solving the block three-by-three saddle point problems, and by analyzing the spectrum of the corresponding preconditioned matrix, we get that it has at most four distinct eigenvalues. Secondly, for the needs of practical applications, we also propose the inexact version of the above preconditioner for solving the block three-by-three saddle point problems, and through the analysis of the spectral properties of the corresponding preconditioned matrix, we obtain the bounds of its eigenvalues. In addition, we also study the choices of the (approximately) optimal parameters in the above inexact preconditioner. Finally, numerical experiments are performed to demonstrate the effectiveness of our proposed inexact preconditioner compared with the existing block preconditioners studied recently for the block three-by-three saddle point problems. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we are concerned with the parameterized least squares inverse eigenvalue problems for the case that the number of parameters to be constructed is less than the number of prescribed realizable eigenvalues. Through equivalent transformation, the original problem becomes a nonlinear least squares problem associated with a specific over-determined mapping defined between a Riemannian manifold and a Euclidean space. We propose the Riemannian two-step perturbed Gauss-Newton method combined with a specific second-order nonmonotone backtracking line search technique for solving general nonlinear least squares problem on Riemannian manifold. Global convergence of this algorithm is discussed under some mild assumptions. Meanwhile, a cubical convergence rate is obtained under injectivity of the differential of the underlying map and zero residue of this map at an accumulation point. To apply the proposed method to solving the parameterized least squares inverse eigenvalue problems, exact solution of the perturbed Riemannian Gauss-Newton equation is constructed. Finally, numerical experiments show the efficiency of the proposed method.(c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new class of unilateral variational models appearing in the theory of poroelasticity is introduced and studied. A poroelastic medium consists of solid phase and pores saturated with a Newtonian fluid. The medium contains a fluid-driven crack, which is subjected to non-penetration between the opposite crack faces. The fully coupled poroelastic system includes elliptic-parabolic governing equations under the unilateral constraint. Well-posedness of the corresponding variational inequality is established based on the Rothe semi-discretization in time, after subsequent passing time step to zero. The NLCP-formulation of non-penetration conditions is given which is useful for a semi-smooth Newton solution strategy. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Cordero, AliciaGarrido, NeusTorregrosa, Juan R.Chicharro, Francisco I....
15页
查看更多>>摘要：In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family is carried out on polynomial systems by selecting different weight functions and comparing the results obtained in each case. This study shows the applicability of the multidimensional dynamical analysis in order to select the methods of the family with the best stability properties. (c) 2020 Elsevier B.V. All rights reserved.
NSTL
Elsevier