Numerical Linear Algebra with Applications最新文献_第2页

The nearest graph Laplacian in Frobenius norm 弗罗贝尼斯规范中的最近图拉普拉卡方

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-22 DOI: 10.1002/nla.2578

Kazuhiro Sato, Masato Suzuki

引用次数: 0

An improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems 大规模无约束非凸问题的改进型下降佩里型算法及其在图像复原问题中的应用

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-13 DOI: 10.1002/nla.2577

Xiaoliang Wang, Jian Lv, Na Xu

{"title":"An improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems","authors":"Xiaoliang Wang, Jian Lv, Na Xu","doi":"10.1002/nla.2577","DOIUrl":"https://doi.org/10.1002/nla.2577","url":null,"abstract":"Conjugate gradient methods are much effective for large‐scale unconstrained optimization problems by their simple computations and low memory requirements. The Perry conjugate gradient method has been considered to be one of the most efficient methods in the context of unconstrained minimization. However, a globally convergent result for general functions has not been established yet. In this paper, an improved three‐term Perry‐type algorithm is proposed which automatically satisfies the sufficient descent property independent of the accuracy of line search strategy. Under the standard Wolfe line search technique and a modified secant condition, the proposed algorithm is globally convergent for general nonlinear functions without convexity assumption. Numerical results compared with the Perry method for stability, two modified Perry‐type conjugate gradient methods and two effective three‐term conjugate gradient methods for large‐scale problems up to 300,000 dimensions indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems. Additionally, we also apply it to some image restoration problems.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611535","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

Solving a class of infinite‐dimensional tensor eigenvalue problems by translational invariant tensor ring approximations 用平移不变张量环近似法解决一类无限维张量特征值问题

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-10 DOI: 10.1002/nla.2573

Roel Van Beeumen, Lana Periša, Daniel Kressner, Chao Yang

引用次数: 0

Randomized low‐rank approximation of parameter‐dependent matrices 参数相关矩阵的随机低阶近似

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-09 DOI: 10.1002/nla.2576

Daniel Kressner, Hei Yin Lam

{"title":"Randomized low‐rank approximation of parameter‐dependent matrices","authors":"Daniel Kressner, Hei Yin Lam","doi":"10.1002/nla.2576","DOIUrl":"https://doi.org/10.1002/nla.2576","url":null,"abstract":"This work considers the low‐rank approximation of a matrix depending on a parameter in a compact set . Application areas that give rise to such problems include computational statistics and dynamical systems. Randomized algorithms are an increasingly popular approach for performing low‐rank approximation and they usually proceed by multiplying the matrix with random dimension reduction matrices (DRMs). Applying such algorithms directly to would involve different, independent DRMs for every , which is not only expensive but also leads to inherently non‐smooth approximations. In this work, we propose to use constant DRMs, that is, is multiplied with the same DRM for every . The resulting parameter‐dependent extensions of two popular randomized algorithms, the randomized singular value decomposition and the generalized Nyström method, are computationally attractive, especially when admits an affine linear decomposition with respect to . We perform a probabilistic analysis for both algorithms, deriving bounds on the expected value as well as failure probabilities for the approximation error when using Gaussian random DRMs. Both, the theoretical results and numerical experiments, show that the use of constant DRMs does not impair their effectiveness; our methods reliably return quasi‐best low‐rank approximations.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573194","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

Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems 针对高频亥姆霍兹问题的𝒟ℋ2矩阵的内存高效压缩技术

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-05 DOI: 10.1002/nla.2575

Steffen Börm, Janne Henningsen

引用次数: 0

Nonnegative low multi‐rank third‐order tensor approximation via transformation 通过变换实现非负低多阶三阶张量逼近

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-05 DOI: 10.1002/nla.2574

Guang‐Jing Song, Yexun Hu, Cobi Xu, Michael K. Ng

{"title":"Nonnegative low multi‐rank third‐order tensor approximation via transformation","authors":"Guang‐Jing Song, Yexun Hu, Cobi Xu, Michael K. Ng","doi":"10.1002/nla.2574","DOIUrl":"https://doi.org/10.1002/nla.2574","url":null,"abstract":"The main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573014","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

Error bounds for the approximation of matrix functions with rational Krylov methods 用有理克雷洛夫方法逼近矩阵函数的误差边界

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-07-02 DOI: 10.1002/nla.2571

Igor Simunec

引用次数: 0

Mass‐lumping discretization and solvers for distributed elliptic optimal control problems 分布式椭圆最优控制问题的质量块离散化和求解器

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-06-27 DOI: 10.1002/nla.2564

Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang

{"title":"Mass‐lumping discretization and solvers for distributed elliptic optimal control problems","authors":"Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang","doi":"10.1002/nla.2564","DOIUrl":"https://doi.org/10.1002/nla.2564","url":null,"abstract":"The purpose of this article is to investigate the effects of the use of mass‐lumping in the finite element discretization with mesh size of the reduced first‐order optimality system arising from a standard tracking‐type, distributed elliptic optimal control problem with regularization, involving a regularization (cost) parameter on which the solution depends. We show that mass‐lumping will not affect the error between the desired state and the computed finite element state , but will lead to a Schur‐complement system that allows for a fast matrix‐by‐vector multiplication. We show that the use of the Schur‐complement preconditioned conjugate gradient method in a nested iteration setting leads to an asymptotically optimal solver with respect to the complexity. While the proposed approach is applicable independently of the regularity of the given target, our particular interest is in discontinuous desired states that do not belong to the state space. However, the corresponding control belongs to whereas the cost as . This motivates to use in order to balance the error and the maximal costs we are willing to accept. This can be embedded into a nested iteration process on a sequence of refined finite element meshes in order to control the error and the cost simultaneously.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509810","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

Anderson acceleration with approximate calculations: Applications to scientific computing 安德森加速近似计算：科学计算的应用

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-05-10 DOI: 10.1002/nla.2562

Massimiliano Lupo Pasini, M. Paul Laiu

{"title":"Anderson acceleration with approximate calculations: Applications to scientific computing","authors":"Massimiliano Lupo Pasini, M. Paul Laiu","doi":"10.1002/nla.2562","DOIUrl":"https://doi.org/10.1002/nla.2562","url":null,"abstract":"SummaryWe provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least‐squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed‐point iterations arising from the Richardson's scheme to solve linear systems with open‐source benchmark matrices with various preconditioners and (ii) non‐linear deterministic fixed‐point iterations arising from non‐linear time‐dependent Boltzmann equations.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927055","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 sampling greedy average regularized Kaczmarz method for tensor recovery 用于张量恢复的采样贪婪平均正则化卡兹马兹方法

IF 4.3 3区数学

Numerical Linear Algebra with Applications Pub Date : 2024-05-07 DOI: 10.1002/nla.2560

Xiaoqing Zhang, Xiaofeng Guo, Jianyu Pan

引用次数: 0