INTERVAL GAUSSIAN ELIMINATION WITH PIVOT TIGHTENING

We present a method by which the breakdown of the interval Gaussian elimination caused by division of an interval containing zero can be avoided for some classes of matrices. These include the inverse nonnegative matrices, the totally nonnegative matrices, and the inverse $M$-matrices--all classes w...

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Veröffentlicht in:	SIAM journal on matrix analysis and applications 2009-01, Vol.30 (4), p.1761-1772
1. Verfasser:	GARLOFF, Jürgen
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Algorithms Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We present a method by which the breakdown of the interval Gaussian elimination caused by division of an interval containing zero can be avoided for some classes of matrices. These include the inverse nonnegative matrices, the totally nonnegative matrices, and the inverse $M$-matrices--all classes with identically signed inverses. The approach consists of a tightening of the interval pivot by determining the exact range of the pivot over the matrix interval.
ISSN:	0895-4798 1095-7162
DOI:	10.1137/080729621