TY - JOUR
T1 - A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems
AU - Li, Ren Cang
AU - Ye, Qiang
PY - 2004
Y1 - 2004
N2 - We present a Krylov subspace-type projection method for a quadratic matrix polynomial λ 2I -λA - B that works directly with A and B without going through any linearization. We discuss a special case when one matrix is a low rank perturbation of the other matrix. We also apply the method to solve quadratically constrained linear least squares problem through a reformulation of Gander, Golub, and von Matt as a quadratic eigenvalue problem, and we demonstrate the effectiveness of this approach. Numerical examples are given to illustrate the efficiency of the algorithms.
AB - We present a Krylov subspace-type projection method for a quadratic matrix polynomial λ 2I -λA - B that works directly with A and B without going through any linearization. We discuss a special case when one matrix is a low rank perturbation of the other matrix. We also apply the method to solve quadratically constrained linear least squares problem through a reformulation of Gander, Golub, and von Matt as a quadratic eigenvalue problem, and we demonstrate the effectiveness of this approach. Numerical examples are given to illustrate the efficiency of the algorithms.
KW - Krylov subspace
KW - Least squares problem
KW - Quadratic constraint
KW - Quadratic eigenvalue problem
KW - Quadratic matrix polynomial
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U2 - 10.1137/S0895479802409390
DO - 10.1137/S0895479802409390
M3 - Article
AN - SCOPUS:1842865580
SN - 0895-4798
VL - 25
SP - 405
EP - 428
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 2
ER -