JournalszaaVol. 19, No. 4pp. 1047–1055

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

Let M(n,R)M(n, \mathbb R) be the set of real positive definite symmetric (n×n)(n \times n)-matrices equipped with the Euclidean norm, and let AM(n,R)A \in M(n, \mathbb R). Let L(n,R)L(n, \mathbb R) be the set of all real non-degenerate lower-triangular (n×n)(n \times n)-matrices equipped with the Euclidean norm, and let L:M(n,R)L(n,R)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 LULU-decomposition. We give an effective upper estimate for L(A)\|L’(A)\|.

Cite this article

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

DOI 10.4171/ZAA/997