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Titolo:
ON THE STABILITY OF CHOLESKY FACTORIZATION FOR SYMMETRICAL QUASIDEFINITE SYSTEMS
Autore:
GILL PE; SAUNDERS MA; SHINNERL JR;
Indirizzi:
UNIV CALIF SAN DIEGO,DEPT MATH LA JOLLA CA 92093 STANFORD UNIV,DEPT OPERAT RES STANFORD CA 94305
Titolo Testata:
SIAM journal on matrix analysis and applications
fascicolo: 1, volume: 17, anno: 1996,
pagine: 35 - 46
SICI:
0895-4798(1996)17:1<35:OTSOCF>2.0.ZU;2-K
Fonte:
ISI
Lingua:
ENG
Soggetto:
INDEFINITE;
Keywords:
SYSTEMS; SYMMETRICAL QUASIDEFINITE (SQD) SYSTEMS; UNSYMMETRIC POSITIVE-DEFINITE SYSTEMS; BACKWARD STABILITY; CONDITION NUMBER; BARRIER METHODS; LINEAR PROGRAMMING;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
15
Recensione:
Indirizzi per estratti:
Citazione:
P.E. Gill et al., "ON THE STABILITY OF CHOLESKY FACTORIZATION FOR SYMMETRICAL QUASIDEFINITE SYSTEMS", SIAM journal on matrix analysis and applications, 17(1), 1996, pp. 35-46

Abstract

Sparse linear equations Kd = r are considered, where K is a speciallystructured symmetric indefinite matrix that arises in numerical optimization and elsewhere. Under certain conditions, K is quasidefinite. The Cholesky factorization PKPT = LDL(T) is then known to exist for anypermutation P, even though D is indefinite. Quasidefinite matrices have been used successfully by Vanderbei within barrier methods for linear and quadratic programming. An advantage is that for a sequence of K's, P may be chosen once and for all to optimize the sparsity of L, asin the positive-definite case. A preliminary stability analysis is developed here. It is observed that a quasidefinite matrix is closely related to an unsymmetric positive-definite matrix, for which an LDM(T) factorization exists. Using the Golub and Van Loan analysis of the latter, conditions are derived under which Cholesky factorization is stable for quasidefinite systems. Some numerical results confirm the predictions.

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Documento generato il 18/09/20 alle ore 15:38:24