On the perturbation of LU and Cholesky factors

In a recent paper, Chang and Paige have shown that the usualperturbation bounds for Cholesky factors can systematicallyoverestimate the errors. In this note we sharpen their resultsand extend them to the factors of the LU decomposition. Theresults are based on a new formula for the first-order termsof the error in the factors. ^* This report is available by anonymous ftp from thales.cs.umd.eduin the directory pub/reports.