Numerische Mathematik

, Volume 62, Issue 1, pp 539–555

Estimating the matrixp-norm


  • Nicholas J. Higham
    • Nuffield Science Research Fellow, Department of MathematicsUniversity of Manchester

DOI: 10.1007/BF01396242

Cite this article as:
Higham, N.J. Numer. Math. (1992) 62: 539. doi:10.1007/BF01396242


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 ‖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)


Copyright information

© Springer-Verlag 1992