The Cholesky method for interval data
type: Item
instance of: scholarly article
title: The Cholesky method for interval data
zbMATH Open document ID: 0796.65032
DOI: 10.1016/0024-3795(93)90120-D
author: Günter Mayer
author: Gotz Alefeld
published in: Linear Algebra and its Applications
publication date: 1994-10-10T00:00:00Z
review text: The interval Cholesky method is established to compute bounds of the solution set of a linear system \(Ax=b\), where it is assumed that \(A\) is symmetric and positive definite and where \(A\) and \(b\) vary within certain bounds. The method is defined as direct interval counter part to the well-known standard non-interval method, and hence, it is applied to the system in interval form, that is, to \(A^ Ix=b^ I\). The usual decomposition, \(A=LL^ T\) where \(L\) is a lower triangular matrix with positive diagonal entries can be gained only in a weaker form in the interval case, i.e., \(A^ I = L^ I(L^ I)^ T\). Beyond that, a second procedure is shown to deliver the same bounds as the first one. Finally, conditions are derived that guarantee the feasibility of the method, which means that division by zero does not occur.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 540063
zbMATH Keywords: interval arithmetic
zbMATH Keywords: interval Cholesky method
zbMATH Keywords: bounds of the solution
zbMATH Keywords: linear system
zbMATH Keywords: feasibility
reviewed by: H. Ratschek
MaRDI profile type: Publication
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Wikidata QID: Q126421866
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description: scientific article; zbMATH DE number 540063