# On a Local Lipschitz Constant of the Maps Related to $LU$-Decomposition

### Z. Balanov

Bar-Ilan University, Ramat Gan, Israel### Wieslaw Krawcewicz

University of Alberta, Edmonton, Canada### A. Kushkuley

Acton, USA### P. P. Zabrejko

The Academy of Sciences of Belarus, Minsk, Belarus

## Abstract

Let $M(n,R)$ be the set of real positive definite symmetric $(n×n)$-matrices equipped with the Euclidean norm, and let $A∈M(n,R)$. Let $L(n,R)$ be the set of all real non-degenerate lower-triangular $(n×n)$-matrices equipped with the Euclidean norm, and let $L:M(n,R)→L(n,R)$ be a (differentiable) map assigning to a positive definite symmetric matrix its lower-triangular factor in the $LU$-decomposition. We give an effective upper estimate for $∥L’(A)∥$.

## Cite this article

Z. Balanov, Wieslaw Krawcewicz, A. Kushkuley, P. P. Zabrejko, On a Local Lipschitz Constant of the Maps Related to $LU$-Decomposition. Z. Anal. Anwend. 19 (2000), no. 4, pp. 1047–1055

DOI 10.4171/ZAA/997