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

Zalman Balanov | Zendy; Wiesław Krawcewicz | Zendy; Alexander Kushkuley | Zendy; Petr P. Zabrejko | Zendy

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

Author(s) -

Zalman Balanov,

Wiesław Krawcewicz,

Alexander Kushkuley,

Petr P. Zabrejko

Publication year - 2000

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/997

Subject(s) - constant (computer programming) , lipschitz continuity , decomposition , mathematics , lipschitz domain , mathematical analysis , pure mathematics , computer science , chemistry , programming language , organic chemistry

Let M(n, R) be the set of real positive definite symmetric (n x n)-matrices equipped with the Euclidean norm, and let A E M(n, IR). Let L(n, R) be the set of all real non-degenerate lower-triangular (n x 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 lowertriangular factor in the LU-decomposition. We give an effective upper estimate for IIL'(A)II.

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