2014•tub.dok (Hamburg University of Technology)Requires access

Verified Bounds for the p-Norm Condition Number.

Siegfried M. Rump

Abstract

Methods to compute verified error bounds for the p-norm condition number of a matrix are discussed for p ∈ 1,2,∞ and the Frobenius norm. We consider the cases of a real or complex, point or interval input matrix. In the latter case the condition number of all matrices within the interval matrix are bounded. A special method for extremely illconditioned matrices is derived as well. Numerical results suggest that the quality of the bounds corresponds to the fact that the condition number of the condition number is the condition number.

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Key concepts: Condition number, Mathematics, Matrix norm, Norm (philosophy), Bounded function, Matrix (chemical analysis), Interval (graph theory), Complex matrix