## 2006.15: Computing the Condition Number of Tridiagonal and Diagonal-Plus-Semiseparable Matrices in Linear Time

2006.15:
Gareth I. Hargreaves
(2006)
*Computing the Condition Number of Tridiagonal and
Diagonal-Plus-Semiseparable Matrices in Linear Time.*
SIAM Journal On Matrix Analysis and Applications, 27 (3).
pp. 801-820.
ISSN 1095-7162

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PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 243 Kb |

DOI: 10.1137/040606636

## Abstract

For an $n \times n$ tridiagonal matrix we exploit the structure of its QR factorization to devise two new algorithms for computing the 1-norm condition number in $O(n)$ operations. The algorithms avoid underflow and overflow, and are simpler than existing algorithms since tests are not required for degenerate cases. An error analysis of the first algorithm is given, while the second algorithm is shown to be competitive in speed with existing algorithms. We then turn our attention to an $n \times n$ diagonal-plus-semiseparable matrix, $A$, for which several algorithms have recently been developed to solve $Ax=b$ in $O(n)$ operations. We again exploit the QR factorization of the matrix to present an algorithm that computes the 1-norm condition number in $O(n)$ operations.

Item Type: | Article |
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Uncontrolled Keywords: | condition number, tridiagonal matrix, diagonal-plus-semiseparable matrix, QR factorization |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.15 |

Deposited By: | Nick Higham |

Deposited On: | 16 February 2006 |

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