查看更多>>摘要：In this work, based on a finite difference scheme, we propose the weak Galerkin (WG) method for solving time-fractional biharmonic equations. Theoretically and numerically, the optimal error estimates for semi-discrete and fully discrete schemes have been investigated. Based on mathematical induction, stability is discussed for the fully discrete scheme that depends on the initial value and the source term. Numerical experiments are provided to confirm the theoretical claims made by the proposed schemes. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we investigate the number of failed components in an operating coherent system. We assume that its components are of multiple types. That is, the system consists of components having nonidentical failure time distributions. We extend the results which are well-known in the literature for k-out-of-n systems. We formulate the optimization problem to determine the optimal values of the number of components of each type together with their arrangement in the system. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The main objective in the present manuscript is to consider approximations of functions defined on the unit circle by Laurent polynomials derived from certain combinations of kernel polynomials of orthogonal polynomials on the unit circle. The method that we employ is based on a modification of the least squares method. The modification adopted here simplifies considerably the determinations of the coefficients in the combinations. Numerical examples show that this modified technique still leads to very good approximations. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision. This framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low-and high-precision evaluations. In this paper we consider the case where the domain of the optimization problem is an abstract metric space. Assumptions about differentiability or even continuity will not be used in the general algorithm based on Inexact Restoration. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A new derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that takes advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a lattice factorization based matrix extension method for constructing the causal FIR symmetric paraunitary filter banks (PUFBs) whose filters H-k (z) , k = 0, 1, ... , M - 1 satisfy the pairwise mirror image (PMI) property, i.e. the condition H-k (z) = HM-1-k (-z) , k = 0, 1, ... , M - 1. And, based on the extension method, we provide a method for constructing compactly supported symmetric orthog-onal wavelets. Firstly, for a given symmetric real-valued M-orthogonal filter H0(z), we propose an algorithm for factorizing a Laurent polynomial matrix composed of polyphase components of the filter pair {H0(z), H0(-z)} into the product of lattice factors and constant matrix. Secondly, based on the lattice factorization algorithm, we propose a method for the causal symmetric PU extension with PMI property of the given Laurent polynomial matrix. This method provides a lattice structure for fast implementation of the resulting symmetric PMI PUFB. Thirdly, we provide a method for constructing compactly supported symmetric orthogonal wavelets by the causal symmetric PMI PU extension. Lastly, several examples are provided to illustrate the construction method proposed in this paper. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, combining the Newton method with matrix splitting technique, a class of Newton-based matrix splitting iteration methods is presented to solve the weakly nonlinear system with some special matrices. Theoretical analysis shows that this kind of iteration method for some special matrices is convergent under suitable conditions. Numerical results show that this kind of iteration method is feasible and effective for the weakly nonlinear system. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we first propose different combination methods to compute the Cauchy principal value integrals of oscillatory Bessel functions. By special transformations, the considered integrals are converted to finite integrals and infinite integrals. Then, the finite integrals can be calculated through the Filon-type method, the Clenshaw-Curtis- Filon method and the Clenshaw-Curtis-Filon-type method, respectively. We compute the infinite integral through the numerical steepest descent method. Moreover, the error analysis with respect to frequency omega is given through theoretical analysis. Eventually, we present several numerical experiments which are in accord with our analysis. Particularly, the accuracy can be improved by either using more nodes or adding more derivatives interpolation at endpoints. The accuracy will increase drastically with the growth of frequency omega if both the number of nodes and interpolated multiplicity are fixed. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we propose two new iterative schemes for finding an element of the set of solutions of a pseudo-monotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. The weak and strong convergence theorems are presented. The advantage of the proposed algorithms is that they do not require prior knowledge of the Lipschitz constant of the variational inequality mapping and only compute one projection onto a feasible set per iteration as well as without using the sequentially weakly continuity of the associated mapping. Under additional strong pseudo-monotonicity and Lipschitz continuity assumptions, we obtain also an R-linear convergence rate of the proposed algorithm. Finally, some numerical examples are given to illustrate the effectiveness of the algorithms. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we establish multiobjective approximate gradient projection (MAGP) and linear multiobjective approximate gradient projection (LMAGP) sequential optimality conditions without constraint qualification for multiobjective constrained optimization problems. Further, we introduce constraint qualifications under which a point that satisfies established optimality conditions also satisfies Karush-Kuhn-Tucker optimality conditions. Such constraint qualifications are called strict constraint qualifications. We discuss the relationship between introduced constraint qualifications and validate it by suitable examples. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Low-rank matrix recovery is an ill-posed problem increasingly involved and treated vitally in various fields such as statistics, bioinformatics, machine learning and computer vision. Robust Principle Component Analysis (RPCA) is recently presented as a 2-terms convex optimization model to solve this problem. In this paper a new 3-terms convex model arising from RPCA is proposed to recover the low-rank components from polluted or incomplete observation data. This new model possesses three regularization terms to reduce the ill-posedness of the recovery problem. Essential difficulty in algorithm derivation is how to deal with the non-smooth terms. The ALM method is introduced to solve the original 2-terms RPCA model with convergence guarantee. However, for solving the proposed 3-terms model, its convergence is no longer guaranteed. As a different approach based on fixed point theory, we introduce the proximity operator to handle nonsmoothness, and consequently a new algorithm derived from Fixed-Point Proximity Algorithm (FPPA) is proposed with convergence analysis. Numerical experiments on the problems of RPCA and Motion Capture Data Refinement (MCDR) demonstrate the outstripping effectiveness and efficiency of the proposed algorithm. (c) 2022 Elsevier B.V. All rights reserved.
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