Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix

Higham, Nicholas J. (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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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 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Nick Higham
Date Deposited:	25 Jan 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/693

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