## 2006.150: Estimating the matrix p-norm

2006.150:
Nicholas J. Higham
(1992)
*Estimating the matrix p-norm.*
Numerische Mathematik, 62.
pp. 539-555.
ISSN 0945-3245

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DOI: 10.1007/BF01396242

## Abstract

The H\"older $p$-norm of an $m \times n$ matrix has no explicit representation unless $p=1$,~$2$ or $\infty$. 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 estimation flavour. The algorithm nearly always computes a $p$-norm estimate correct to the specified accuracy, and the estimate is always within a factor $n^{1-1/p}$ 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.

Item Type: | Article |
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Uncontrolled Keywords: | H\"older norm, $p$-norm, matrix norm, condition number estimation, LAPACK. |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.150 |

Deposited By: | Miss Louise Stait |

Deposited On: | 28 June 2006 |

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