N A ] 2 2 O ct 2 02 0 AN OVERVIEW OF BLOCK GRAM-SCHMIDT METHODS AND THEIR STABILITY PROPERTIES
N A ] 2 2 O ct 2 02 0 AN OVERVIEW OF BLOCK GRAM-SCHMIDT METHODS AND THEIR STABILITY PROPERTIES
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N A ] 2 2 Oct 2 02 0 BLOCK GRAM-SCHMIDT 方法及其稳定性特性概述
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Thomas
中科院分区：
文献类型：
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作者：
E. Carson;Kathryn Lund;M. Rozložník;Stephen;Thomas
.块Gram-Schmidt算法包括许多科学计算应用中的基本内核，但对于许多常用的变体，对其稳定性的严格处理仍然是开放的。本综述提供了块Gram-Schmidt算法的全面分类，特别是那些用于Krylov子空间方法中的一次构建一个块向量的正交基的算法。收集所有已知的稳定性结果，并总结或阐明重要的减少通信的变体的新结果。提供了各种各样的数值说明，沿着Matlab代码，用于在存储库https://github.com/katlund/BlockStab上公开再现结果。一些开放的问题进行了讨论，并提供了一个附录，其中包含所有算法类型设置在一个统一的方式。
. Block Gram-Schmidt algorithms comprise essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This survey provides a comprehensive categorization of block Gram-Schmidt algorithms, especially those used in Krylov subspace methods to build orthonormal bases one block vector at a time. All known stability results are assembled, and new results are summarized or conjectured for important communication-reducing variants. A diverse array of numerical illustrations are presented, along with the Matlab code for reproducing the results in a publicly available at repository https://github.com/katlund/BlockStab. A number of open problems are discussed, and an appendix containing all algorithms type-set in a uniform fashion is provided.
DOI：
10.1137/140973463
发表时间：
2014-12
期刊：
SIAM J. Matrix Anal. Appl.
影响因子：
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作者：
A. Frommer;S. Güttel;M. Schweitzer
通讯作者：
A. Frommer;S. Güttel;M. Schweitzer