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Implementation for LAPACK of a Block Algorithm for Matrix 1-Norm Estimation ∗

By Sheung Hun, Cheng Nicholas and J. Higham


We describe double precision and complex*16 Fortran 77 implementations, in LAPACK style, of a block matrix 1-norm estimator of Higham and Tisseur. This estimator differs from that underlying the existing LAPACK code, xLACON, in that it iterates with a matrix with t columns, where t ≥ 1 is a parameter, rather than with a vector, and so the basic computational kernel is level 3 BLAS operations. Our experiments with random matrices on a Sun SPARCStation Ultra-5 show that with t = 2 or 4 the new code offers better estimates than xLACON with a similar execution time. Moreover, with t> 2, estimates exact over 95 % and 75 % of the time are achieved for the real and complex version respectively, with execution time growing much slower than t. We recommend this new code be included as an auxiliary routine in LAPACK to complement the existing LAPACK routine xLACON, upon which the various drivers should still be based for compatibility reasons.

Year: 2001
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