UPDATING THE INVERSE OF A MATRIX
UPDATING THE INVERSE OF A MATRIX
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DOI：
10.1137/1031049
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发表时间：
1989-06-01
期刊：
影响因子：
10.2
通讯作者：
HAGER, WW
中科院分区：
文献类型：
--
作者：
HAGER, WW
Sherman-Morrison-Woodbury公式将小阶扰动后矩阵的逆与原始矩阵的逆联系起来。介绍了这些公式的历史，并讨论了在统计、网络、结构分析、渐近分析、优化和偏微分方程中的各种应用。Sherman-Morrison-Woodbury公式用原始矩阵的逆表示经过小秩扰动后的矩阵的逆。本文回顾了这些公式的历史，并分析了这些公式的一些应用
The Sherman–Morrison–Woodbury formulas relate the inverse of a matrix after a small-rank perturbation to the inverse of the original matrix. The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed. The Sherman-Morrison-Woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix. This paper surveys the history of these formulas and we examine some applications where these formulas are helpful