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2007.8: Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix

2007.8: Nicholas J. Higham (1986) Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix. SIAM Journal of Scientific and Statistical Computing, 7 (1). pp. 150-165. ISSN 1064-8275

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DOI: 10.1137/0907011

Abstract

Let A be a tridiagonal matrix of order n. We show that it is possible to compute and hence condo (A), in O(n) operations. Several algorithms which perform this task are given and their numerical properties are investigated. If A is also positive definite then I[A-[[o can be computed as the norm of the solution to a positive definite tridiagonal linear system whose coeffcient matrix is closely related to A. We show how this computation can be carried out in parallel with the solution of a linear system Ax b. In particular we describe some simple modifications to the LINPACK routine SPTSL which enable this routine to compute condt (A), efficiently, in addition to solving Ax b.

Item Type:Article
Uncontrolled Keywords:matrix condition number, tridiagonal matrix, positive definite matrix, LINPACK
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2007.8
Deposited By:Nick Higham
Deposited On:25 January 2007

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