Numerische Mathematik

, Volume 62, Issue 1, pp 539-555

First online:

Estimating the matrixp-norm

  • Nicholas J. HighamAffiliated withNuffield Science Research Fellow, Department of Mathematics, University of Manchester

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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 factorn 1−1/p of ‖A‖ p . 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.

Mathematical Subject Classification (1991)