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An optimal circulant preconditioner for Toeplitz systems. (English) Zbl 0646.65042
Given a Toeplitz matrix A, this note presents a very simple algorithm for computing a circulant preconditioner C that minimizes \(\| C-A\|_ F\). Four examples are given in which C performs better than a preconditioner proposed earlier by G. Strang [Stud. Appl. Math. 74, 171-176 (1986; Zbl 0621.65025)].
Reviewer: P.C.Hansen

MSC:
65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
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