You are here: MIMS > EPrints
MIMS EPrints

## 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

Full text available as:

 PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader243 Kb

## 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 condition number, tridiagonal matrix, diagonal-plus-semiseparable matrix, QR factorization MSC 2000 > 15 Linear and multilinear algebra; matrix theoryMSC 2000 > 65 Numerical analysis 2006.15 Nick Higham 16 February 2006