Estimating the matrixp-norm |
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Authors: | Nicholas J. Higham |
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Affiliation: | (1) Nuffield Science Research Fellow, Department of Mathematics, University of Manchester, M13 9PL Manchester, UK |
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Abstract: | Summary The Hölderp-norm of anm×n matrix has no explicit representation unlessp=1,2 or . It is shown here that thep-norm can be estimated reliably inO(mn) operations. A generalization of the power method is used, with a starting vector determined by a technique with a condition estimation flavour. The algorithm nearly always computes ap-norm estimate correct to the specified accuracy, and the estimate is always within a factorn1–1/p of Ap. As a by-product, a new way is obtained to estimate the 2-norm of a rectangular matrix; this method is more general and produces better estimates in practice than a similar technique of Cline, Conn and Van Loan. |
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Keywords: | 65F35 |
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