Strathprints logo
Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Large growth factors in Gaussian elimination with pivoting

Higham, D.J. and Higham, N.J. (1989) Large growth factors in Gaussian elimination with pivoting. SIAM Journal on Matrix Analysis and Applications, 10 (2). pp. 155-164. ISSN 0895-4798

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

The growth factor plays an important role in the error analysis of Gaussian elimination. It is well known that when partial pivoting or complete pivoting is used the growth factor is usually small, but it can be large. The examples of large growth usually quoted involve contrived matrices that are unlikely to occur in practice. We present real and complex $n imes n$ matrices arising from practical applications that, for any pivoting strategy, yield growth factors bounded below by $n / 2$ and $n$, respectively. These matrices enable us to improve the known lower bounds on the largest possible growth factor in the case of complete pivoting. For partial pivoting, we classify the set of real matrices for which the growth factor is $2^{n - 1} $. Finally, we show that large element growth does not necessarily lead to a large backward error in the solution of a particular linear system, and we comment on the practical implications of this result.

Item type: Article
ID code: 213
Keywords: Gaussian elimination, growth factor, partial pivoting, complete pivoting, backward error analysis, stability, numerical mathematics, Mathematics, Analysis
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 08 Mar 2006
    Last modified: 04 Sep 2014 09:52
    URI: http://strathprints.strath.ac.uk/id/eprint/213

    Actions (login required)

    View Item