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Unsymmetric Positive Definite Linear Systems

Author
Golub, Gene H.; Van Loan, Charles
Abstract
Is it necessary to pivot when solving an unsymmetric positive definite linear system $Ax = b?$ Define $T = (A + A^{T})/2$ and $S=(A+AA^{T})/2$. It is shown that pivoting is unnecessary if the quantitity is $\Vert S T^{-1} S \Vert_{2}/ \Vert A \Vert_{2}$ is suitably small with respect to the working machine precision.
Date Issued
1978-09Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR78-352
Type
technical report