Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Condition numbers and their condition numbers

Higham, D.J. (1995) Condition numbers and their condition numbers. Linear Algebra and Its Applications, 214. pp. 193-214. ISSN 0024-3795

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

Abstract

Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also analyzed. The sensitivity of the condition number itself is then investigated, and we obtain sharp examples of Demmel's general result that for certain problems in numerical analysis 'the condition number of the condition number is the condition number.' Finally, upper bounds are derived for the sensitivity of componentwise condition numbers.