A linear system solver based on a modified Krylov subspace method for breakdown recovery
The authors present a scheme based on a modified Krylov subspace approach to Lanczos' biorthogonalization method of the solution of nonsymmetric linear systems. When the scheme breaks down it is replaced by a modified dual Krylov subspace which is the sum of the original subspace and a new Krylov subspace which depends on a new start vector and the original matrix. Based on this strategy, they develop a practical algorithm for solving linear systems (the MLAN/QM algorithm) which also incorporates the residual quasi-minimization proposed by \textit{R. W. Freund} and \textit{N. M. Nachtigal} [Numer. Math. 60, No. 3, 315-339 (1991; Zbl 0754.65034)]. The algorithm is presented in some computational detail. Convergence bounds for the method are presented as well as numerical results to show its effectiveness.
scientific article; zbMATH DE number 915392
scientific article