A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates

2024/06/21 by Stefan Güttel, Yuji Nakatsukasa, Güttel, Stefan +5 · 1 citation
Engineering · Mathematics · #65F20 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2406.15120

openalex publication_date 2024/06/21 · openalex created_date 2024/06/25 · openalex updated_date 2026/07/28

Abstract

We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squares problems. The resulting algorithm can be dramatically faster than solving the modified least squares problem from scratch, just like the speedup enabled by Sherman--Morrison--Woodbury for solving linear systems with low-rank modifications.

Cited by

• Instability of the Sherman-Morrison formula and stabilization by iterative refinement

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