Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems
This paper is concerned with the solution sequences of systems of linear equations where the coefficient matrices are nonsingular nonsymmetric Toeplitz matrices arising from a generating function of the Wiener class. A technique for the construction of optimal trigonometric preconditioners of the corresponding normal equation is described. It is shown that the spectrum of the preconditioned matrix is clustered at 1 so that the preconditioned conjugate gradient method applied to the normal equation converges superlinearly. Numerical tests confirm the theoretical results.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 1370034
scientific article