Numerical Linear Algebra with Applications最新文献_第4页

Total positivity and high relative accuracy for several classes of Hankel matrices 几类汉克尔矩阵的全正性和高相对精度

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-02-20 DOI: 10.1002/nla.2550

E. Mainar, J.M. Peña, B. Rubio

引用次数: 0

Preconditioned discontinuous Galerkin method and convection-diffusion-reaction problems with guaranteed bounds to resulting spectra 预处理非连续伽勒金方法和对流-扩散-反应问题与结果谱的保证边界

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-02-08 DOI: 10.1002/nla.2549

Liya Gaynutdinova, Martin Ladecký, Ivana Pultarová, Miloslav Vlasák, Jan Zeman

{"title":"Preconditioned discontinuous Galerkin method and convection-diffusion-reaction problems with guaranteed bounds to resulting spectra","authors":"Liya Gaynutdinova, Martin Ladecký, Ivana Pultarová, Miloslav Vlasák, Jan Zeman","doi":"10.1002/nla.2549","DOIUrl":"https://doi.org/10.1002/nla.2549","url":null,"abstract":"This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or discontinuous Galerkin methods. We expand on the approach introduced by Gergelits et al. and adapt it to the more general settings, assuming that both the original and preconditioning matrices are composed of sparse matrices of very low ranks, representing local contributions to the global matrices. When applied to a symmetric problem, the method provides bounds to all individual eigenvalues of the preconditioned matrix. We show that this preconditioning strategy works not only for Galerkin discretization, but also for the discontinuous Galerkin discretization, where local contributions are associated with individual edges of the triangulation. In the case of nonsymmetric problems, the method yields guaranteed bounds to real and imaginary parts of the resulting eigenvalues. We include some numerical experiments illustrating the method and its implementation, showcasing its effectiveness for the two variants of discretized (convection-)diffusion-reaction problems.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Normalized Newton method to solve generalized tensor eigenvalue problems 解决广义张量特征值问题的归一化牛顿法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-01-09 DOI: 10.1002/nla.2547

Mehri Pakmanesh, Hamidreza Afshin, Masoud Hajarian

引用次数: 0

Matrix‐less methods for the spectral approximation of large non‐Hermitian Toeplitz matrices: A concise theoretical analysis and a numerical study 大型非ermitian Toeplitz 矩阵谱近似的无矩阵方法：简明理论分析与数值研究

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-01-04 DOI: 10.1002/nla.2545

M. Bogoya, Sven-Erik Ekström, S. Serra‐Capizzano, P. Vassalos

{"title":"Matrix‐less methods for the spectral approximation of large non‐Hermitian Toeplitz matrices: A concise theoretical analysis and a numerical study","authors":"M. Bogoya, Sven-Erik Ekström, S. Serra‐Capizzano, P. Vassalos","doi":"10.1002/nla.2545","DOIUrl":"https://doi.org/10.1002/nla.2545","url":null,"abstract":"It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non‐Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non‐Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix‐size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects; for example, non‐Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high‐precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Practical sketching-based randomized tensor ring decomposition 基于草图的实用随机张量环分解

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-01-02 DOI: 10.1002/nla.2548

Yajie Yu, Hanyu Li

引用次数: 0

Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material 强异质材料孔弹性问题的稳健分块对角线预处理器

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-12-26 DOI: 10.1002/nla.2546

Tomáš Luber, Stanislav Sysala

引用次数: 0

Generalizing reduction-based algebraic multigrid 推广基于还原的代数多网格

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-12-18 DOI: 10.1002/nla.2543

Tareq Zaman, Nicolas Nytko, Ali Taghibakhshi, Scott MacLachlan, Luke Olson, Matthew West

{"title":"Generalizing reduction-based algebraic multigrid","authors":"Tareq Zaman, Nicolas Nytko, Ali Taghibakhshi, Scott MacLachlan, Luke Olson, Matthew West","doi":"10.1002/nla.2543","DOIUrl":"https://doi.org/10.1002/nla.2543","url":null,"abstract":"Algebraic multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction-based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two-level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine- and coarse-grid degrees of freedom. MacLachlan and Saad (SISC 2007) proved that the AMGr method yields provably robust two-level convergence for symmetric and positive-definite matrices that are diagonally dominant, with a convergence factor bounded as a function of a coarsening parameter. However, when applying AMGr algorithms to matrices that are not diagonally dominant, not only do the convergence factor bounds not hold, but measured performance is notably degraded. Here, we present modifications to the classical AMGr algorithm that improve its performance on matrices that are not diagonally dominant, making use of strength of connection, sparse approximate inverse (SPAI) techniques, and interpolation truncation and rescaling, to improve robustness while maintaining control of the algorithmic costs. We present numerical results demonstrating the robustness of this approach for both classical isotropic diffusion problems and for non-diagonally dominant systems coming from anisotropic diffusion.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138824407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

An iterative algorithm for low-rank tensor completion problem with sparse noise and missing values 具有稀疏噪声和缺失值的低阶张量补全问题的迭代算法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-12-17 DOI: 10.1002/nla.2544

Jianheng Chen, Wen Huang

引用次数: 0

Practical alternating least squares for tensor ring decomposition 张量环分解的实用交替最小二乘法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-12-10 DOI: 10.1002/nla.2542

Yajie Yu, Hanyu Li

{"title":"Practical alternating least squares for tensor ring decomposition","authors":"Yajie Yu, Hanyu Li","doi":"10.1002/nla.2542","DOIUrl":"https://doi.org/10.1002/nla.2542","url":null,"abstract":"Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional and higher-order data. A well-known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large-scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS-based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR-cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138632252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Preconditioned weighted full orothogonalization method for solving singular linear systems from PageRank problems PageRank问题中奇异线性系统的预条件加权全正交化方法

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-11-10 DOI: 10.1002/nla.2541

Zhao‐Li Shen, Bruno Carpentieri, Chun Wen, Jian‐Jun Wang, Stefano Serra‐Capizzano, Shi‐Ping Du

{"title":"Preconditioned weighted full orothogonalization method for solving singular linear systems from PageRank problems","authors":"Zhao‐Li Shen, Bruno Carpentieri, Chun Wen, Jian‐Jun Wang, Stefano Serra‐Capizzano, Shi‐Ping Du","doi":"10.1002/nla.2541","DOIUrl":"https://doi.org/10.1002/nla.2541","url":null,"abstract":"Abstract The PageRank model, which was first proposed by Google for its web search engine application, has since become a popular computational tool in a wide range of scientific fields, including chemistry, bioinformatics, neuroscience, bibliometrics, social networks, and others. PageRank calculations necessitate the use of fast computational techniques with low algorithmic and memory complexity. In recent years, much attention has been paid to Krylov subspace algorithms for solving difficult PageRank linear systems, such as those with large damping parameters close to one. In this article, we examine the full orthogonalization method (FOM). We present a convergence study of the method that extends and clarifies part of the conclusions reached in Zhang et al. (J Comput Appl Math. 2016; 296:397–409.). Furthermore, we demonstrate that FOM is breakdown free when solving singular PageRank linear systems with index one and we investigate the effect of using weighted inner‐products instead of conventional inner‐products in the orthonormalization procedure on FOM convergence. Finally, we develop a shifted polynomial preconditioner that takes advantage of the special structure of the PageRank linear system and has a good ability to cluster most of the eigenvalues, making it a good choice for an iterative method like FOM or GMRES. Numerical experiments are presented to support the theoretical findings and to evaluate the performance of the new weighted preconditioned FOM PageRank solver in comparison to other established solvers for this class of problem, including conventional stationary methods, hybrid combinations of stationary and Krylov subspace methods, and multi‐step splitting strategies.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135138404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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