Improved backward error bounds for LU and Cholesky factorizations
New backward error bounds for LU and Cholesky factorizations are provided. To get these new bounds, the main ingradient is a refinement of the well-known Lemma 8.4 from \textit{N. J. Higham} [Accuracy and stability of numerical algorithms. 2nd ed. Philadelphia, PA: SIAM (2002; Zbl 1011.65010)] via some careful rounding error analysis of sums of one floating-point number and \(n-1\) real numbers.
scientific article; zbMATH DE number 6356192