On the generation of Krylov subspace bases
The authors discuss different ways for the construction of Krylov subspace bases used in the generalized minimal residual (GMRES) method for solving systems of linear equations \(A x = b\) approximately. Especially, the construction by means of shifted and scaled versions of the standard Chebyshev polynomials of the first kind and by means of scaled Newton polynomials is considered. Some numerical examples are presented. For different matrices \(A\) the condition numbers for the scaled power basis, two kinds of Newton bases and the Chebyshev polynomial basis are compared. Furthermore, the influence of the condition number of the Krylov subspace bases on the convergence of the GMRES method is illustrated. The discussed approaches are also applicable to Krylov subspace methods for eigenvalue computations and the evaluation of matrix functions.
scientific article; zbMATH DE number 6055249
scientific article