Journal of Computational and Applied Mathematics最新文献_第3页

A new subspace iteration algorithm for solving generalized eigenvalue problems in vibration analysis

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-14 DOI: 10.1016/j.cam.2025.116622

Biyi Wang , Hengbin An , Hehu Xie , Zeyao Mo

{"title":"A new subspace iteration algorithm for solving generalized eigenvalue problems in vibration analysis","authors":"Biyi Wang , Hengbin An , Hehu Xie , Zeyao Mo","doi":"10.1016/j.cam.2025.116622","DOIUrl":"10.1016/j.cam.2025.116622","url":null,"abstract":"<div><div>Large scale generalized eigenvalue problems (GEP) arise in many applications, such as the vibration analysis, quantum mechanics, electronic structure calculation. A class of subspace iteration method, the generalized Chebyshev–Davidson (gCD) algorithm, was recently proposed to solve GEP. In the gCD algorithm, the Chebyshev polynomial filter technique is incorporated in the subspace iteration. One of the advantages of the gCD algorithm is that it only concerns matrix vector product, making it suitable for solving large-scale problems. In this paper, based on gCD algorithm, a new subspace iteration algorithm is constructed. In the proposed algorithm, we combine the Chebyshev filter and inexact Rayleigh quotient iteration techniques to enlarge the subspace in the iteration, and the obtained algorithm is named as Chebyshev-RQI subspace (CRS) method. Numerical results for both two dimensional and three dimensional vibration analysis problems show that CRS algorithm is more effective than gCD algorithm measured by iteration numbers and computing time. Specifically, when these two methods are used to compute the smallest 20 eigenpairs of the tested vibration models, CRS converges at least 3.9 times faster than gCD measured by number of iteration and up to 2.5 times faster than gCD measured by solution time. Furthermore, CRS algorithm is more robust than gCD because in some cases, gCD cannot converge while CRS always converges for all test cases.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116622"},"PeriodicalIF":2.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Polynomial homotopy methods for the equally spaced sparse interpolation problem with jump

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-13 DOI: 10.1016/j.cam.2025.116623

Panpan Zhao , Bo Yu , Libin Jiao

引用次数: 0

Global accelerated Hermitian and skew–Hermitian splitting preconditioner for the solution of discrete Stokes problems

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-10 DOI: 10.1016/j.cam.2025.116620

A. Badahmane , A. Ratnani , H. Sadok

{"title":"Global accelerated Hermitian and skew–Hermitian splitting preconditioner for the solution of discrete Stokes problems","authors":"A. Badahmane , A. Ratnani , H. Sadok","doi":"10.1016/j.cam.2025.116620","DOIUrl":"10.1016/j.cam.2025.116620","url":null,"abstract":"<div><div>In fluid mechanics, numerous applications necessitate solving a sequence of linear systems. These systems typically arise from discretizing the Stokes equations using mixed-finite element methods. The matrices that result from this process often exhibit a saddle point structure, which makes the iterative solution of preconditioned linear systems challenging. To effectively solve the large scale and ill-conditioned linear systems, it is necessary to implement efficient linear solvers. We present a global approach, specifically the preconditioned global conjugate gradient (PGCG), aimed at enhancing the performance of preconditioned Hermitian and skew–Hermitian splitting preconditioner <span><math><mrow><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>P</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub><mo>)</mo></mrow></math></span> and accelerated Hermitian and skew–Hermitian splitting preconditioner <span><math><mrow><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>A</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub><mo>)</mo></mrow></math></span>. The new preconditioners can be utilized to expedite the convergence of the generalized minimal residual (GMRES) method. We evaluate the effectiveness of the preconditioned iterative methods by considering the Central Processing Unit (<span><math><mi>CPU</mi></math></span>) times and numbers of the <span><math><mi>P</mi></math></span>GMRES iterations. The numerical results indicate that incorporating <span><math><mi>P</mi></math></span>GCG method improves the performance of the preconditioners <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>P</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>A</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116620"},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Greedy Kaczmarz methods for nonlinear equation

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-08 DOI: 10.1016/j.cam.2025.116630

Li Liu, Wei-Guo Li, Wen-Di Bao, Li-Li Xing

引用次数: 0

Fast numerical derivatives of univariate functions on non-uniform grids

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-08 DOI: 10.1016/j.cam.2025.116619

Nadaniela Egidi, Josephin Giacomini, Pierluigi Maponi

引用次数: 0

A sharpening median filter for Cauchy noise with wavelet based regularization

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-07 DOI: 10.1016/j.cam.2025.116625

Xiao Ai , Guoxi Ni , Tieyong Zeng

引用次数: 0

Solution of linear ill-posed operator equations by modified truncated singular value expansion

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-07 DOI: 10.1016/j.cam.2025.116621

Laura Dykes , Mykhailo Kuian , Thomas Mach , Silvia Noschese , Lothar Reichel

{"title":"Solution of linear ill-posed operator equations by modified truncated singular value expansion","authors":"Laura Dykes , Mykhailo Kuian , Thomas Mach , Silvia Noschese , Lothar Reichel","doi":"10.1016/j.cam.2025.116621","DOIUrl":"10.1016/j.cam.2025.116621","url":null,"abstract":"<div><div>In much of the literature on the solution of linear ill-posed operator equations in a Hilbert space, the operator equation first is discretized, then the discretized operator is regularized, and finally, the computed solution of the regularized discrete problem is projected into a Hilbert space. In order for this solution approach to give an accurate approximate solution, the regularization method has to correspond to a meaningful analogue in Hilbert space. Moreover, the regularization method chosen may only be applicable to certain linear ill-posed operator equations. However, these issues typically are not discussed in the literature on solution methods based on discretization. One approach to circumvent this difficulty is to avoid discretization. This paper describes how regularization by a modified truncated singular value decomposition introduced in Noschese and Reichel (2014) for finite-dimensional problems can be extended to operator equations. In finite dimensions, this regularization method yields approximate solutions of higher quality than standard truncated singular value decomposition. Our analysis in a Hilbert space setting is of practical interest, because the solution method presented avoids the introduction of discretization errors during the solution process, since we compute regularized solutions without discretization by using the program package Chebfun. While this paper focuses on a particular regularization method, the analysis presented and Chebfun also can be applied to other regularization techniques.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116621"},"PeriodicalIF":2.1,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

New upper bounds for the q-numerical radii of 2×2 operator matrices

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-06 DOI: 10.1016/j.cam.2025.116618

Fuad Kittaneh , M.H.M. Rashid

引用次数: 0

Optimal error estimates of second-order weighted virtual element method for nonlinear coupled prey–predator equation

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-06 DOI: 10.1016/j.cam.2025.116617

Yanping Chen , Shanshan Peng

{"title":"Optimal error estimates of second-order weighted virtual element method for nonlinear coupled prey–predator equation","authors":"Yanping Chen , Shanshan Peng","doi":"10.1016/j.cam.2025.116617","DOIUrl":"10.1016/j.cam.2025.116617","url":null,"abstract":"<div><div>In this paper, we develop a numerical method for solving the nonlinear coupled prey–predator equation on arbitrary polygonal meshes, employing the virtual element method for spatial discretization and a second-order weighted method for temporal discretization. We rigorously establish the existence, uniqueness and convergence of solutions using Schaefer’s fixed point theorem. Moreover, we derive an optimal error estimate in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm that is independent of any spatial–temporal grid ratio constraints. This approach eliminates the need for the time semi-discrete system that would otherwise be introduced by temporal–spatial error splitting techniques, thereby streamlining the computational process. By adjusting the weighted parameter <span><math><mi>θ</mi></math></span>, the second-order weighted scheme seamlessly transitions to classic methods such as Crank–Nicolson (<span><math><mrow><mi>θ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>) and two-step backward differentiation formula method (<span><math><mrow><mi>θ</mi><mo>=</mo><mn>1</mn></mrow></math></span>). Finally, numerical experiments confirm the validity of our theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116617"},"PeriodicalIF":2.1,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of a generalized MASSOR method for saddle point problems

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-06 DOI: 10.1016/j.cam.2025.116626

Changfeng Ma , Xiaojuan Yu

引用次数: 0