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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 4, 2000, pp. 1047–1055
DOI: 10.4171/ZAA/997

Published online: 2000-12-31

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

Z. Balanov[1], Wieslaw Krawcewicz[2], A. Kushkuley[3] and P. P. Zabrejko[4]

(1) Bar-Ilan University, Ramat Gan, Israel
(2) University of Alberta, Edmonton, Canada
(3) Acton, USA
(4) The Academy of Sciences of Belarus, Minsk, Belarus

Let $M(n, \mathbb R)$ be the set of real positive definite symmetric $(n \times n)$-matrices equipped with the Euclidean norm, and let $A \in M(n, \mathbb R)$. Let $L(n, \mathbb R)$ be the set of all real non-degenerate lower-triangular $(n \times n)$-matrices equipped with the Euclidean norm, and let $L : M(n, \mathbb R) \to L(n, \mathbb R)$ 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 $\|L’(A)\|$.

Keywords: Lipschitz constant, $LU$-decomposition, Schur and Hadamard inequalities

Balanov Z., Krawcewicz Wieslaw, Kushkuley A., Zabrejko P. P.: On a Local Lipschitz Constant of the Maps Related to $LU$-Decomposition. Z. Anal. Anwend. 19 (2000), 1047-1055. doi: 10.4171/ZAA/997