SIAM Journal on Matrix Analysis and Applications最新文献_第4页

A Block Householder–Based Algorithm for the QR Decomposition of Hierarchical Matrices 分层矩阵 QR 分解的基于分块豪斯德的算法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-04-19 DOI: 10.1137/22m1544555

Vincent Griem, Sabine Le Borne

引用次数: 0

Analyzing Vector Orthogonalization Algorithms 分析矢量正交化算法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-04-12 DOI: 10.1137/22m1519523

Christopher C. Paige

引用次数: 0

Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices 某些稀疏矩阵块编码的显式量子电路

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-03-12 DOI: 10.1137/22m1484298

Daan Camps, Lin Lin, Roel Van Beeumen, Chao Yang

{"title":"Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices","authors":"Daan Camps, Lin Lin, Roel Van Beeumen, Chao Yang","doi":"10.1137/22m1484298","DOIUrl":"https://doi.org/10.1137/22m1484298","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 801-827, March 2024. Abstract. Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest [math] in a larger unitary transformation [math] that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of [math], which is difficult in general, and not trivial even for well structured sparse matrices. In this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Partial Degeneration of Tensors 张量的部分退化

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-03-11 DOI: 10.1137/23m1554898

Matthias Christandl, Fulvio Gesmundo, Vladimir Lysikov, Vincent Steffan

{"title":"Partial Degeneration of Tensors","authors":"Matthias Christandl, Fulvio Gesmundo, Vladimir Lysikov, Vincent Steffan","doi":"10.1137/23m1554898","DOIUrl":"https://doi.org/10.1137/23m1554898","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 771-800, March 2024. Abstract. Tensors are often studied by introducing preorders such as restriction and degeneration. The former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local linear maps may vary along a curve, and the resulting tensor is expressed as a limit along this curve. In this work, we introduce and study partial degeneration, a special version of degeneration where one of the local linear maps is constant while the others vary along a curve. Motivated by algebraic complexity, quantum entanglement, and tensor networks, we present constructions based on matrix multiplication tensors and find examples by making a connection to the theory of prehomogeneous tensor spaces. We highlight the subtleties of this new notion by showing obstruction and classification results for the unit tensor. To this end, we study the notion of aided rank, a natural generalization of tensor rank. The existence of partial degenerations gives strong upper bounds on the aided rank of a tensor, which allows one to turn degenerations into restrictions. In particular, we present several examples, based on the W-tensor and the Coppersmith–Winograd tensors, where lower bounds on aided rank provide obstructions to the existence of certain partial degenerations.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"87 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Adaptive Rational Krylov Methods for Exponential Runge–Kutta Integrators 指数 Runge-Kutta 积分器的自适应理性克雷洛夫方法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-03-05 DOI: 10.1137/23m1559439

Kai Bergermann, Martin Stoll

{"title":"Adaptive Rational Krylov Methods for Exponential Runge–Kutta Integrators","authors":"Kai Bergermann, Martin Stoll","doi":"10.1137/23m1559439","DOIUrl":"https://doi.org/10.1137/23m1559439","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 744-770, March 2024. Abstract. We consider the solution of large stiff systems of ODEs with explicit exponential Runge–Kutta integrators. These problems arise from semidiscretized semilinear parabolic PDEs on continuous domains or on inherently discrete graph domains. A series of results reduces the requirement of computing linear combinations of [math]-functions in exponential integrators to the approximation of the action of a smaller number of matrix exponentials on certain vectors. State-of-the-art computational methods use polynomial Krylov subspaces of adaptive size for this task. They have the drawback that the required number of Krylov subspace iterations to obtain a desired tolerance increases drastically with the spectral radius of the discrete linear differential operator, e.g., the problem size. We present an approach that leverages rational Krylov subspace methods promising superior approximation qualities. We prove a novel a posteriori error estimate of rational Krylov approximations to the action of the matrix exponential on vectors for single time points, which allows for an adaptive approach similar to existing polynomial Krylov techniques. We discuss pole selection and the efficient solution of the arising sequences of shifted linear systems by direct and preconditioned iterative solvers. Numerical experiments show that our method outperforms the state of the art for sufficiently large spectral radii of the discrete linear differential operators. The key to this are approximately constant numbers of rational Krylov iterations, which enable a near-linear scaling of the runtime with respect to the problem size.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"32 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals nlTGCR：基于共轭残差的一类非线性加速程序

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-29 DOI: 10.1137/23m1576360

Huan He, Ziyuan Tang, Shifan Zhao, Yousef Saad, Yuanzhe Xi

引用次数: 0

An Escape Time Formulation for Subgraph Detection and Partitioning of Directed Graphs 有向图的子图检测和分割的逃逸时间公式

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-26 DOI: 10.1137/23m1553790

Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, Braxton Osting

{"title":"An Escape Time Formulation for Subgraph Detection and Partitioning of Directed Graphs","authors":"Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, Braxton Osting","doi":"10.1137/23m1553790","DOIUrl":"https://doi.org/10.1137/23m1553790","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 685-711, March 2024. Abstract. We provide a rearrangement based algorithm for detection of subgraphs of k vertices with long escape times for directed or undirected networks that is not combinatorially complex to compute. Complementing other notions of densest subgraphs and graph cuts, our method is based on the mean hitting time required for a random walker to leave a designated set and hit the complement. We provide a new relaxation of this notion of hitting time on a given subgraph and use that relaxation to construct a subgraph detection algorithm that can be computed easily and a generalization to K-partitioning schemes. Using a modification of the subgraph detector on each component, we propose a graph partitioner that identifies regions where random walks live for comparably large times. Importantly, our method implicitly respects the directed nature of the data for directed graphs while also being applicable to undirected graphs. We apply the partitioning method for community detection to a large class of models and real-world data sets.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"134 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139968531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Randomized Joint Diagonalization of Symmetric Matrices 对称矩阵的随机联合对角化

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-26 DOI: 10.1137/22m1541265

Haoze He, Daniel Kressner

引用次数: 0

Singular Value Decomposition of Dual Matrices and its Application to Traveling Wave Identification in the Brain 双矩阵的奇异值分解及其在大脑游波识别中的应用

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-12 DOI: 10.1137/23m1556642

Tong Wei, Weiyang Ding, Yimin Wei

{"title":"Singular Value Decomposition of Dual Matrices and its Application to Traveling Wave Identification in the Brain","authors":"Tong Wei, Weiyang Ding, Yimin Wei","doi":"10.1137/23m1556642","DOIUrl":"https://doi.org/10.1137/23m1556642","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 634-660, March 2024. Abstract. Matrix factorizations in dual number algebra, a hypercomplex number system, have been applied to kinematics, spatial mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves using the singular value decomposition (SVD) of dual matrices in this paper. Theoretically, we propose the compact dual singular value decomposition (CDSVD) of dual complex matrices with explicit expressions as well as a necessary and sufficient condition for its existence. Furthermore, based on the CDSVD, we report on the optimal solution to the best rank-[math] approximation under a newly defined quasi-metric in the dual complex number system. The CDSVD is also related to the dual Moore–Penrose generalized inverse. Numerically, comparisons with other available algorithms are conducted, which indicate less computational costs of our proposed CDSVD. In addition, the infinitesimal part of the CDSVD can identify the true rank of the original matrix from the noise-added matrix, but the classical SVD cannot. Next, we employ experiments on simulated time-series data and a road monitoring video to demonstrate the beneficial effect of the infinitesimal parts of dual matrices in spatiotemporal pattern identification. Finally, we apply this approach to the large-scale brain functional magnetic resonance imaging data, identify three kinds of traveling waves, and further validate the consistency between our analytical results and the current knowledge of cerebral cortex function.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"23 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Speeding Up Krylov Subspace Methods for Computing [math] via Randomization 通过随机化加速计算[数学]的克雷洛夫子空间方法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-09 DOI: 10.1137/22m1543458

Alice Cortinovis, Daniel Kressner, Yuji Nakatsukasa

引用次数: 0