Numerical Linear Algebra with Applications最新文献

A Family of Inertial Three‐Term CGPMs for Large‐Scale Nonlinear Pseudo‐Monotone Equations With Convex Constraints 具有凸约束条件的大规模非线性伪单调方程的惯性三期 CGPM 族

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-09-11 DOI: 10.1002/nla.2589

Jinbao Jian, Qiongxuan Huang, Jianghua Yin, Guodong Ma

{"title":"A Family of Inertial Three‐Term CGPMs for Large‐Scale Nonlinear Pseudo‐Monotone Equations With Convex Constraints","authors":"Jinbao Jian, Qiongxuan Huang, Jianghua Yin, Guodong Ma","doi":"10.1002/nla.2589","DOIUrl":"https://doi.org/10.1002/nla.2589","url":null,"abstract":"This article presents and analyzes a family of three‐term conjugate gradient projection methods with the inertial technique for solving large‐scale nonlinear pseudo‐monotone equations with convex constraints. The generated search direction exhibits good properties independent of line searches. The global convergence of the family is proved without the Lipschitz continuity of the underlying mapping. Furthermore, under the locally Lipschitz continuity assumption, we conduct a thorough analysis related to the asymptotic and non‐asymptotic global convergence rates in terms of iteration complexity. To our knowledge, this is the first iteration‐complexity analysis for inertial gradient‐type projection methods, in the literature, under such a assumption. Numerical experiments demonstrate the computational efficiency of the family, showing its superiority over three existing inertial methods. Finally, we apply the proposed family to solve practical problems such as ‐regularized logistic regression, sparse signal restoration and image restoration problems, highlighting its effectiveness and potential for real‐world applications.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222838","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

Signal and image reconstruction with a double parameter Hager–Zhang‐type conjugate gradient method for system of nonlinear equations 用双参数哈格-张式共轭梯度法重建非线性方程系统的信号和图像

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-09-09 DOI: 10.1002/nla.2583

Kabiru Ahmed, Mohammed Yusuf Waziri, Abubakar Sani Halilu, Salisu Murtala, Habibu Abdullahi

{"title":"Signal and image reconstruction with a double parameter Hager–Zhang‐type conjugate gradient method for system of nonlinear equations","authors":"Kabiru Ahmed, Mohammed Yusuf Waziri, Abubakar Sani Halilu, Salisu Murtala, Habibu Abdullahi","doi":"10.1002/nla.2583","DOIUrl":"https://doi.org/10.1002/nla.2583","url":null,"abstract":"The one parameter conjugate gradient method by Hager and Zhang (Pac J Optim, 2(1):35–58, 2006) represents a family of descent iterative methods for solving large‐scale minimization problems. The nonnegative parameter of the scheme determines the weight of conjugacy and descent, and by extension, the numerical performance of the method. The scheme, however, does not converge globally for general nonlinear functions, and when the parameter approaches 0, the scheme reduces to the conjugate gradient method by Hestenes and Stiefel (J Res Nat Bur Stand, 49:409–436, 1952), which in practical sense does not perform well due to the jamming phenomenon. By carrying out eigenvalue analysis of an adaptive two parameter Hager–Zhang type method, a new scheme is presented for system of monotone nonlinear equations with its application in compressed sensing. The proposed scheme was inspired by nice attributes of the Hager–Zhang method and the various schemes designed with double parameters. The scheme is also applicable to nonsmooth nonlinear problems. Using fundamental assumptions, analysis of the global convergence of the scheme is conducted and preliminary report of numerical experiments carried out with the scheme and some recent methods indicate that the scheme is promising.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222839","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

Superlinear Krylov convergence under streamline diffusion FEM for convection‐dominated elliptic operators 对流主导椭圆算子流线扩散有限元下的超线性克雷洛夫收敛

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-09-02 DOI: 10.1002/nla.2586

János Karátson

引用次数: 0

On rank‐revealing QR factorizations of quaternion matrices 关于四元数矩阵的秩揭示 QR 因式分解

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-08-29 DOI: 10.1002/nla.2585

Qiaohua Liu, Chuge Li

{"title":"On rank‐revealing QR factorizations of quaternion matrices","authors":"Qiaohua Liu, Chuge Li","doi":"10.1002/nla.2585","DOIUrl":"https://doi.org/10.1002/nla.2585","url":null,"abstract":"This work develops theories and algorithms for computing rank‐revealing QR factorizations (qRRQR) of quaternion matrices. First, by introducing a novel quaternion determinant, a quasi‐Cramer's rule is established to investigate the existence theory of the qRRQR factorization of an quaternion matrix . The proposed theory provides a systematic approach for selecting linearly independent columns of in order to ensure that the resulting diagonal blocks , of the R‐factor possess rank revealing properties in both spectral and Frobenius norms. Secondly, by increasing the quaternion determinants of in each iteration by a factor of at least (), a greedy algorithm with cyclic block pivoting strategy is derived to implement the qRRQR factorization. This algorithm costs about real floating‐point operations, which is as nearly efficient as quaternion QR with column pivoting for most problems. It also shows the effectiveness and reliability, particularly when dealing with a class of quaternion Kahan matrices. Furthermore, two improved greedy algorithms are proposed. Experiments evaluations are conducted on synthetic data as well as color image compression and quaternion signals denoising. The experimental results validate the usefulness and efficiency of our improved algorithm across various scenarios.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222841","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

Probabilistic perturbation bounds of matrix decompositions 矩阵分解的概率扰动边界

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-08-28 DOI: 10.1002/nla.2582

Petko H. Petkov

引用次数: 0

Dynamically accelerating the power iteration with momentum 动态加速动力迭代

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-08-24 DOI: 10.1002/nla.2584

Christian Austin, Sara Pollock, Yunrong Zhu

{"title":"Dynamically accelerating the power iteration with momentum","authors":"Christian Austin, Sara Pollock, Yunrong Zhu","doi":"10.1002/nla.2584","DOIUrl":"https://doi.org/10.1002/nla.2584","url":null,"abstract":"In this article, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be applied to real diagonalizable matrices, is provably convergent with acceleration in the symmetric case, and does not require a priori spectral knowledge. We review and extend background results on previously developed static momentum accelerations for the power iteration through the connection between the momentum accelerated iteration and the standard power iteration applied to an augmented matrix. We show that the augmented matrix is defective for the optimal parameter choice. We then present our dynamic method which updates the momentum parameter at each iteration based on the Rayleigh quotient and two previous residuals. We present convergence and stability theory for the method by considering a power‐like method consisting of multiplying an initial vector by a sequence of augmented matrices. We demonstrate the developed method on a number of benchmark problems, and see that it outperforms both the power iteration and often the static momentum acceleration with optimal parameter choice. Finally, we present and demonstrate an explicit extension of the algorithm to inverse power iterations.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222842","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 rational‐Chebyshev projection method for nonlinear eigenvalue problems 非线性特征值问题的有理-切比雪夫投影法

IF 1.8 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-08-08 DOI: 10.1002/nla.2563

Z. Tang, Yousef Saad

引用次数: 0

Accurate bidiagonal decompositions of Cauchy–Vandermonde matrices of any rank 任意秩 Cauchy-Vandermonde 矩阵的精确对角分解

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-08-07 DOI: 10.1002/nla.2579

Jorge Delgado, Plamen Koev, Ana Marco, José‐Javier Martínez, Juan Manuel Peña, Per‐Olof Persson, Steven Spasov

引用次数: 0

On the efficient preconditioning of the Stokes equations in tight geometries 论狭小几何结构中斯托克斯方程的高效预处理

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-31 DOI: 10.1002/nla.2581

Vladislav Pimanov, Oleg Iliev, Ivan Oseledets, Ekaterina Muravleva

{"title":"On the efficient preconditioning of the Stokes equations in tight geometries","authors":"Vladislav Pimanov, Oleg Iliev, Ivan Oseledets, Ekaterina Muravleva","doi":"10.1002/nla.2581","DOIUrl":"https://doi.org/10.1002/nla.2581","url":null,"abstract":"It is known (see, e.g., [SIAM J. Matrix Anal. Appl. 2014;35(1):143‐173]) that the performance of iterative methods for solving the Stokes problem essentially depends on the quality of the preconditioner for the Schur complement matrix, . In this paper, we consider two preconditioners for : the identity one and the SIMPLE one, and numerically study their performance for solving the Stokes problem in tight geometries. The latter are characterized by a high surface‐to‐volume ratio. We show that for such geometries, can become severely ill‐conditioned, having a very large condition number and a significant portion of non‐unit eigenvalues. As a consequence, the identity matrix, which is broadly used as a preconditioner for solving the Stokes problem in simple geometries, becomes very inefficient. We show that there is a correlation between the surface‐to‐volume ratio and the condition number of : the latter increases with the increase of the former. We show that the condition number of the diffusive SIMPLE‐preconditioned Schur complement matrix remains bounded when the surface‐to‐volume ratio increases, which explains the robust performance of this preconditioner for tight geometries. Further on, we use a direct method to calculate the full spectrum of and show that there is a correlation between the number of its non‐unit eigenvalues and the number of grid points at which no‐slip boundary conditions are prescribed. To illustrate the above findings, we examine the Pressure Schur Complement formulation for staggered finite‐difference discretization of the Stokes equations and solve it with the preconditioned conjugate gradient method. The practical problem which is of interest to us is computing the permeability of tight rocks.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863876","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

Robust tensor recovery via a nonconvex approach with ket augmentation and auto‐weighted strategy 通过 ket 增强和自动加权策略的非凸方法实现稳健的张量恢复

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-30 DOI: 10.1002/nla.2580

Wenhui Xie, Chen Ling, Hongjin He, Lei‐Hong Zhang

引用次数: 0