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 -