TY - GEN

T1 - Krylov subspace methods in the electronic industry

AU - Heres, P.J.

AU - Schilders, W.H.A.

PY - 2006

Y1 - 2006

N2 - In most practical cases, the convergence of the GMRES method applied to a linear
algebraic system Ax -- b is determined by the distribution of eigenvalues of A. In
theory, however, the information about the eigenvalues alone is not sufficient for determining
the convergence. In this paper the previous work of Greenbaum et al. is
extended in the following direction. It is given a complete parametrization of the set
of all pairs {A, b} for which GMRES(A, b) generates the prescribed convergence curve
while the matrix A has the prescribed eigenvalues. Moreover, a characterization of the
right hand sides b for which the GMRES(A, b) converges exactly in m steps, where m
is the degree of the minimal polynomial of A, is given.

AB - In most practical cases, the convergence of the GMRES method applied to a linear
algebraic system Ax -- b is determined by the distribution of eigenvalues of A. In
theory, however, the information about the eigenvalues alone is not sufficient for determining
the convergence. In this paper the previous work of Greenbaum et al. is
extended in the following direction. It is given a complete parametrization of the set
of all pairs {A, b} for which GMRES(A, b) generates the prescribed convergence curve
while the matrix A has the prescribed eigenvalues. Moreover, a characterization of the
right hand sides b for which the GMRES(A, b) converges exactly in m steps, where m
is the degree of the minimal polynomial of A, is given.

U2 - 10.1007/3-540-28073-1_16

DO - 10.1007/3-540-28073-1_16

M3 - Conference contribution

SN - 3-540-28073-1

T3 - Mathematics in Industry

SP - 139

EP - 143

BT - Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004)

A2 - Di Bucchianico, A.

A2 - Mattheij, R.M.M.

A2 - Peletier, M.A.

PB - Springer

CY - Berlin

ER -