Numerical Linear Algebra with Applications最新文献_第10页

QZ algorithm with two‐sided generalized Rayleigh quotient shifts 具有双侧广义瑞利商位移的QZ算法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-11-10 DOI: 10.1002/nla.2475

X. Chen, Hongguo Xu

引用次数: 0

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems 对称广义特征值问题的增强代数子结构

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-10-17 DOI: 10.1002/nla.2473

V. Kalantzis, L. Horesh

{"title":"Enhanced algebraic substructuring for symmetric generalized eigenvalue problems","authors":"V. Kalantzis, L. Horesh","doi":"10.1002/nla.2473","DOIUrl":"https://doi.org/10.1002/nla.2473","url":null,"abstract":"This article proposes a new substructuring algorithm to approximate the algebraically smallest eigenvalues and corresponding eigenvectors of a symmetric positive‐definite matrix pencil (A,M)$$ left(A,Mright) $$ . The proposed approach partitions the graph associated with (A,M)$$ left(A,Mright) $$ into a number of algebraic substructures and builds a Rayleigh–Ritz projection subspace by combining spectral information associated with the interior and interface variables of the algebraic domain. The subspace associated with interior variables is built by computing substructural eigenvectors and truncated Neumann series expansions of resolvent matrices. The subspace associated with interface variables is built by computing eigenvectors and associated leading derivatives of linearized spectral Schur complements. The proposed algorithm can take advantage of multilevel partitionings when the size of the pencil. Experiments performed on problems stemming from discretizations of model problems showcase the efficiency of the proposed algorithm and verify that adding eigenvector derivatives can enhance the overall accuracy of the approximate eigenpairs, especially those associated with eigenvalues located near the origin.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43396741","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

Sine transform based preconditioning techniques for space fractional diffusion equations 基于正弦变换的空间分数扩散方程预处理技术

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-10-07 DOI: 10.1002/nla.2474

H. Qin, Hong-Kui Pang, Hai-wei Sun

引用次数: 2

Three adaptive hybrid derivative‐free projection methods for constrained monotone nonlinear equations and their applications 约束单调非线性方程的三种自适应混合无导数投影方法及其应用

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-10-05 DOI: 10.1002/nla.2471

Peng Liu, Xiaoyu Wu, H. Shao, Yan Zhang, Shuhan Cao

引用次数: 6

On the evaluation of general sparse hybrid linear solvers 关于一般稀疏混合线性解的评价

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-09-28 DOI: 10.1002/nla.2469

Afrah Farea, M. S. Çelebi

{"title":"On the evaluation of general sparse hybrid linear solvers","authors":"Afrah Farea, M. S. Çelebi","doi":"10.1002/nla.2469","DOIUrl":"https://doi.org/10.1002/nla.2469","url":null,"abstract":"General sparse hybrid solvers are commonly used kernels for solving wide range of scientific and engineering problems. This work addresses the current problems of efficiently solving general sparse linear equations with direct/iterative hybrid solvers on many core distributed clusters. We briefly discuss the solution stages of Maphys, HIPS, and PDSLin hybrid solvers for large sparse linear systems with their major algorithmic differences. In this category of solvers, different methods with sophisticated preconditioning algorithms are suggested to solve the trade off between memory and convergence. Such solutions require a certain hierarchical level of parallelism more suitable for modern supercomputers that allow to scale for thousand numbers of processors using Schur complement framework. We study the effect of reordering and analyze the performance, scalability as well as memory for each solve phase of PDSLin, Maphys, and HIPS hybrid solvers using large set of challenging matrices arising from different actual applications and compare the results with SuperLU_DIST direct solver. We specifically focus on the level of parallel mechanisms used by the hybrid solvers and the effect on scalability. Tuning and Analysis Utilities (TAU) is employed to assess the efficient usage of heap memory profile and measuring communication volume. The tests are run on high performance large memory clusters using up to 512 processors.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46771212","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

The analytic connectivity in uniform hypergraphs: Properties and computation 一致超图中的解析连通性：性质与计算

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-09-20 DOI: 10.1002/nla.2468

Chunfeng Cui, Ziyan Luo, L. Qi, Hong Yan

引用次数: 0

Lower and upper bounds of condition number for Vandermonde‐wise matrices and method of fundamental solutions using pseudo radial‐lines Vandermonde矩阵条件数的下界和上界以及使用伪径向线的基本解方法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-09-06 DOI: 10.1002/nla.2466

Li-Ping Zhang, Zi-Cai Li, Ming-Gong Lee, Hung-Tsai Huang

引用次数: 0

Computing f ‐divergences and distances of high‐dimensional probability density functions 计算高维概率密度函数的f -散度和距离

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-09-06 DOI: 10.1002/nla.2467

A. Litvinenko, Y. Marzouk, H. Matthies, M. Scavino, Alessio Spantini

{"title":"Computing f ‐divergences and distances of high‐dimensional probability density functions","authors":"A. Litvinenko, Y. Marzouk, H. Matthies, M. Scavino, Alessio Spantini","doi":"10.1002/nla.2467","DOIUrl":"https://doi.org/10.1002/nla.2467","url":null,"abstract":"Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high‐dimensional random variables. Here the interest is mainly to compute characterizations like the entropy, the Kullback–Leibler divergence, more general f$$ f $$ ‐divergences, or other such characteristics based on the probability density. The density is often not available directly, and it is a computational challenge to just represent it in a numerically feasible fashion in case the dimension is even moderately large. It is an even stronger numerical challenge to then actually compute said characteristics in the high‐dimensional case. In this regard it is proposed to approximate the discretized density in a compressed form, in particular by a low‐rank tensor. This can alternatively be obtained from the corresponding probability characteristic function, or more general representations of the underlying random variable. The mentioned characterizations need point‐wise functions like the logarithm. This normally rather trivial task becomes computationally difficult when the density is approximated in a compressed resp. low‐rank tensor format, as the point values are not directly accessible. The computations become possible by considering the compressed data as an element of an associative, commutative algebra with an inner product, and using matrix algorithms to accomplish the mentioned tasks. The representation as a low‐rank element of a high order tensor space allows to reduce the computational complexity and storage cost from exponential in the dimension to almost linear.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48740288","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: 1

Issue Information 问题信息

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-09-01 DOI: 10.1002/nla.2396

引用次数: 0

Low Tucker rank tensor completion using a symmetric block coordinate descent method 低塔克秩张量补全使用对称块坐标下降方法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2022-08-16 DOI: 10.1002/nla.2464

Quan Yu, Xinzhen Zhang, Yannan Chen, Liqun Qi

引用次数: 7