Estimating the matrix p-norm
نویسنده
چکیده
The H61der p-norm of an m • n matrix has no explicit representation unless p = 1, 2 or ~ . It is shown here that the p-norm can be estimated reliably in O(mn) operations. A generalization of the power method is used, with a starting vector determined by a technique with a condition est imation flavour. The algor i thm nearly always computes a p-norm estimate correct to the specified accuracy, and the estimate is always within a factor n ~ l/p of t[ A lit 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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