Perturbation analysis for block downdating of a Cholesky decomposition
Let the Cholesky decomposition of \(X^ T X\) be \(X^ T X = R^ T R\), where \(R\) is upper triangular. The Cholesky block downdating problem is to determine \(\widetilde{R}\) such that \(\widetilde{R}^ T \widetilde{R} = R^ T R - Z^ T Z\), where \(Z\) is a block of rows from the data matrix \(X\). This paper analyzes the sensitivity of this block downdating problem of the Cholesky factorization. A measure of conditioning for the Cholesky block downdating is presented and compared to the single row downdating case.
scientific article; zbMATH DE number 691552