Picture of virus under microscope

Research under the microscope...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

Explore SIPBS research

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.