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Numerical Linear Algebra with Applications最新文献

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Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation 具有隐式紧缩的块预条件最陡下降特征解的收敛性分析
3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-03-15 DOI: 10.1002/nla.2498
Ming Zhou, Zhaojun Bai, Yunfeng Cai, Klaus Neymeyr
{"title":"Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation","authors":"Ming Zhou, Zhaojun Bai, Yunfeng Cai, Klaus Neymeyr","doi":"10.1002/nla.2498","DOIUrl":"https://doi.org/10.1002/nla.2498","url":null,"abstract":"Abstract Gradient‐type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent iteration with implicit deflation (PSD‐id) is one of such methods. The convergence behavior of the PSD‐id is recently investigated based on the pioneering work of Samokish on the preconditioned steepest descent method (PSD). The resulting non‐asymptotic estimates indicate a superlinear convergence of the PSD‐id under strong assumptions on the initial guess. The present paper utilizes an alternative convergence analysis of the PSD by Neymeyr under much weaker assumptions. We embed Neymeyr's approach into the analysis of the PSD‐id using a restricted formulation of the PSD‐id. More importantly, we extend the new convergence analysis of the PSD‐id to a practically preferred block version of the PSD‐id, or BPSD‐id, and show the cluster robustness of the BPSD‐id. Numerical examples are provided to validate the theoretical estimates.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648575","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
A block Cholesky‐LU‐based QR factorization for rectangular matrices 基于块Cholesky - LU的矩形矩阵QR分解
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-02-25 DOI: 10.1002/nla.2497
S. Le Borne
{"title":"A block Cholesky‐LU‐based QR factorization for rectangular matrices","authors":"S. Le Borne","doi":"10.1002/nla.2497","DOIUrl":"https://doi.org/10.1002/nla.2497","url":null,"abstract":"The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block‐partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well‐known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46945924","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
Asymptotics for the eigenvalues of Toeplitz matrices with a symbol having a power singularity 符号具有幂奇点的Toeplitz矩阵特征值的渐近性
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-02-21 DOI: 10.1002/nla.2496
M. Bogoya, S. Grudsky
{"title":"Asymptotics for the eigenvalues of Toeplitz matrices with a symbol having a power singularity","authors":"M. Bogoya, S. Grudsky","doi":"10.1002/nla.2496","DOIUrl":"https://doi.org/10.1002/nla.2496","url":null,"abstract":"The present work is devoted to the construction of an asymptotic expansion for the eigenvalues of a Toeplitz matrix Tn(a)$$ {T}_n(a) $$ as n$$ n $$ goes to infinity, with a continuous and real‐valued symbol a$$ a $$ having a power singularity of degree γ$$ gamma $$ with 1","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41510287","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
Editorial: Tensor numerical methods and their application in scientific computing and data science 社论：张量数值方法及其在科学计算和数据科学中的应用
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-31 DOI: 10.1002/nla.2493
B. Khoromskij, V. Khoromskaia
{"title":"Editorial: Tensor numerical methods and their application in scientific computing and data science","authors":"B. Khoromskij, V. Khoromskaia","doi":"10.1002/nla.2493","DOIUrl":"https://doi.org/10.1002/nla.2493","url":null,"abstract":",","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49364141","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
Issue Information 问题信息
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-30 DOI: 10.1002/nla.2450
{"title":"Issue Information","authors":"","doi":"10.1002/nla.2450","DOIUrl":"https://doi.org/10.1002/nla.2450","url":null,"abstract":"","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48420131","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
Structure preserving quaternion full orthogonalization method with applications 保结构四元数全正交化方法及其应用
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-28 DOI: 10.1002/nla.2495
Tao Li, Qingwen Wang
{"title":"Structure preserving quaternion full orthogonalization method with applications","authors":"Tao Li, Qingwen Wang","doi":"10.1002/nla.2495","DOIUrl":"https://doi.org/10.1002/nla.2495","url":null,"abstract":"This article proposes a structure‐preserving quaternion full orthogonalization method (QFOM) for solving quaternion linear systems arising from color image restoration. The method is based on the quaternion Arnoldi procedure preserving the quaternion Hessenberg form. Combining with the preconditioning techniques, we further derive a variant of the QFOM for solving the linear systems, which can greatly improve the rate of convergence of QFOM. Numerical experiments on randomly generated data and color image restoration problems illustrate the effectiveness of the proposed algorithms in comparison with some existing methods.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46859199","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: 3
High relative accuracy with some special matrices related to Γ and β functions 与Γ和β函数有关的一些特殊矩阵的高相对精度
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-23 DOI: 10.1002/nla.2494
J. Delgado, J. Peña
{"title":"High relative accuracy with some special matrices related to Γ and β functions","authors":"J. Delgado, J. Peña","doi":"10.1002/nla.2494","DOIUrl":"https://doi.org/10.1002/nla.2494","url":null,"abstract":"For some families of totally positive matrices using Γ$$ Gamma $$ and β$$ beta $$ functions, we provide their bidiagonal factorization. Moreover, when these functions are defined over integers, we prove that the bidiagonal factorization can be computed with high relative accuracy and so we can compute with high relative accuracy their eigenvalues, singular values, inverses and the solutions of some associated linear systems. We provide numerical examples illustrating this high relative accuracy.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48028882","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
Solution methods to the nearest rotation matrix problem in  ℝ3 : A comparative survey 最接近旋转矩阵问题的求解方法:比较综述
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-21 DOI: 10.1002/nla.2492
Soheil Sarabandi, Federico Thomas
{"title":"Solution methods to the nearest rotation matrix problem in  ℝ3 : A comparative survey","authors":"Soheil Sarabandi, Federico Thomas","doi":"10.1002/nla.2492","DOIUrl":"https://doi.org/10.1002/nla.2492","url":null,"abstract":"Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47907040","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
A flexible block classical Gram–Schmidt skeleton with reorthogonalization 具有重正交化的柔性块经典Gram-Schmidt骨架
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-19 DOI: 10.1002/nla.2491
Qinmeng Zou
{"title":"A flexible block classical Gram–Schmidt skeleton with reorthogonalization","authors":"Qinmeng Zou","doi":"10.1002/nla.2491","DOIUrl":"https://doi.org/10.1002/nla.2491","url":null,"abstract":"We investigate a variant of the reorthogonalized block classical Gram–Schmidt method for computing the QR factorization of a full column rank matrix. Our aim is to bound the loss of orthogonality even when the first local QR algorithm is only conditionally stable. In particular, this allows the use of modified Gram–Schmidt instead of Householder transformations as the first local QR algorithm. Numerical experiments confirm the stable behavior of the new variant. We also examine the use of non‐QR local factorization and show by example that the resulting variants, although less stable, may also be applied to ill‐conditioned problems.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43722134","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
Nonconvex optimization for third‐order tensor completion under wavelet transform 小波变换下三阶张量补全的非凸优化
IF 4.3 3区 数学
Numerical Linear Algebra with Applications Pub Date : 2023-01-15 DOI: 10.1002/nla.2489
Quan Yu, Minru Bai
{"title":"Nonconvex optimization for third‐order tensor completion under wavelet transform","authors":"Quan Yu, Minru Bai","doi":"10.1002/nla.2489","DOIUrl":"https://doi.org/10.1002/nla.2489","url":null,"abstract":"The main aim of this paper is to develop a nonconvex optimization model for third‐order tensor completion under wavelet transform. On the one hand, through wavelet transform of frontal slices, we divide a large tensor data into a main part tensor and three detail part tensors, and the elements of these four tensors are about a quarter of the original tensors. Solving these four small tensors can not only improve the operation efficiency, but also better restore the original tensor data. On the other hand, by using concave correction term, we are able to correct for low rank of tubal nuclear norm (TNN) data fidelity term and sparsity of l1$$ {l}_1 $$ ‐norm data fidelity term. We prove that the proposed algorithm can converge to some critical point. Experimental results on image, magnetic resonance imaging and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state‐of‐the‐arts including the TNN and other methods.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2023-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48662560","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
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