A new class of decomposition for symmetric systems
type: Item
instance of: scholarly article
title: A new class of decomposition for symmetric systems
zbMATH Open document ID: 0757.65027
DOI: 10.1016/0093-6413(92)90060-N
author: Jenn-Ching Luo
published in: Mechanics Research Communications
publication date: 1993-01-16T00:00:00Z
review text: A direct method is described, not based upon Gauss elimination, for decomposing a symmetric matrix \(A\) into \(L\), \(D\), \(L^ T\) such that the product \(LDL^ T\) is the inverse of \(A\). The solution \(X\) to the system \(AX=B\) is then computed by three matrix-vector multiplications: \(X=LDL^ TB\). This method has two advantages: The decomposed matrices represent the inverse. The decomposition and matrix-vector multiplications can be transferred into a procedure with fewer degree of data dependence which can be used in a parallel environment.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 92758
zbMATH Keywords: matrix decomposition
zbMATH Keywords: symmetric matrix
zbMATH Keywords: linear system
zbMATH Keywords: matrix inversion
zbMATH Keywords: parallel computation
reviewed by: Horst Hollatz
MaRDI profile type: Publication
full work available at URL: 0093-6413(92)90060-n
OpenAlex ID: W2025992401
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description: scientific article; zbMATH DE number 92758