## 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 |
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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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