Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-10T09:26:05.104Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower bounds for tau coefficients and operator norms using composite matrix norms

Published online by Cambridge University Press:  17 April 2009

Choon Peng Tan
Choon Peng Tan
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur 59100, Malaysia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 49 - 57
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Lancaster, P., Theory of Matrices, (Academic Press, New York, 1969).Google Scholar
[2]Maitre, J. -F., “Norme composée et norme associée généralisée d'une matrice”, Numer. Math. 10 (1967) 132–141.CrossRefGoogle Scholar
[3]Merikoski, J.K., “Lower Bounds for ‖A‖2 by Hölder Norms”, Linear and Multilinear Algebra 9 (1981) 341–344.Google Scholar
[4]Ostrowski, A., “Über Normen von Matrizen”, Math. Z. 63 (1955). 2–18.Google Scholar
[5]Rothblum, U.G. and Tan, C.P., “Upper Bounds on the Maximum Modulus of Subdominant Eigenvalues of Nonegative Matrices”, Linear Algebra Appl. 66 (1985), 45–86.CrossRefGoogle Scholar
[6]Seneta, E. and Tan, C.P., “The Euclidean and Frobenius Ergodicity Coefficients and Spectrum Localization”, Bull. Malaysian Math. Soc. (2) 7 (1984), 1–7.Google Scholar
[7]Tan, C.P., “A Bound Problem in the Modeling of Computer Systems and Queueing Networks”, Mathematical Computer Performance and Reliability, (Iazeolla, G., Courtois, P.J. and Hordijk, A., Eds.) North-Holland, Amsterdam, (1984) 303–311.Google Scholar