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In this paper, our attention is concentrated on the GMRES method for the solution of the system of linear algebraic equations with a nonsymmetric matrix. We perform pre-iterations before starting GMRES and put for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the th powers of eigenvalues of the matrix . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and numerical...
In this paper we compare the numerical performance on a set of ill conditioned problems of several algorithms for linear systems based upon the explicit QR factorization and the implicit LQ factorization associated with the Huang and the modified Huang algorithms in the ABS class. The results indicate that the modified Huang algorithm is generally more accurate than the Huang algorithm and competitive with commercial codes based upon the QR factorization with Householder of Givens reflections. The...
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