Updating the Inverse of a Matrix
Abstract¶
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
Summary¶
Hager surveys and analyzes formulas for updating a matrix inverse after low-rank changes, including relationships to Sherman-Morrison-Woodbury-type identities. The paper is a compact reference for efficient inverse maintenance in numerical linear algebra and optimization algorithms.