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A survey of condition number estimation for triangular matrices. (English) Zbl 0635.65049

Some methods of estimating the condition number of a triangular matrix without actually computing its inverse or singular value decomposition are discussed. They consist of one or two steps of inverse iteration with an appropriately chosen starting vector, possibly applying a matrix whose condition majorizes the actual one. Both upper and lower bounds are computed. Comparisons on randomly chosen data as well as carefully developed difficult cases or counterexamples are given. It is found that the widely used LINPACK estimator performs reasonably well but some other algorithms give better results for a comparable amount of work.
Reviewer: A.Ruhe

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
15A12 Conditioning of matrices
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