TY - JOUR
T1 - An iterated shift-and-invert Arnoldi algorithm for quadratic matrix eigenvalue problems
AU - Ye, Qiang
PY - 2006/1/15
Y1 - 2006/1/15
N2 - For solving the large scale quadratic eigenvalue problem L(λ)x: = (Aλ2 + Bλ + C)x = 0, a direct projection method based on the Krylov subspaces generated by a single matrix A-1B using the standard Arnoldi algorithm is considered. It is shown that, when iteratively combined with the shift-and-invert technique, it results in a fast converging algorithm. The important situations of inexact shift-and-invert are also discussed and numerical examples are presented to illustrate the new method.
AB - For solving the large scale quadratic eigenvalue problem L(λ)x: = (Aλ2 + Bλ + C)x = 0, a direct projection method based on the Krylov subspaces generated by a single matrix A-1B using the standard Arnoldi algorithm is considered. It is shown that, when iteratively combined with the shift-and-invert technique, it results in a fast converging algorithm. The important situations of inexact shift-and-invert are also discussed and numerical examples are presented to illustrate the new method.
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U2 - 10.1016/j.amc.2004.11.015
DO - 10.1016/j.amc.2004.11.015
M3 - Article
AN - SCOPUS:31644442237
SN - 0096-3003
VL - 172
SP - 818
EP - 827
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2 SPEC. ISS.
ER -