TY - JOUR
T1 - A Golub-Kahan-type reduction method for matrix pairs
AU - Hochstenbach, M.E.
AU - Reichel, L.
AU - Yu, X.
PY - 2015
Y1 - 2015
N2 - We describe a novel method for reducing a pair of large matrices {A,B} to a pair of small matrices {H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large linear discrete ill-posed problems are described. In these problems the matrix A represents a discretization of a compact integral operator and B is a regularization matrix.
Keywords: Generalized Golub–Kahan bidiagonalization; Generalized Lanczos bidiagonalization; Generalized Krylov method; Matrix pair decomposition; Ill-posed problem; Tikhonov regularization; Multi-parameter regularization
AB - We describe a novel method for reducing a pair of large matrices {A,B} to a pair of small matrices {H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large linear discrete ill-posed problems are described. In these problems the matrix A represents a discretization of a compact integral operator and B is a regularization matrix.
Keywords: Generalized Golub–Kahan bidiagonalization; Generalized Lanczos bidiagonalization; Generalized Krylov method; Matrix pair decomposition; Ill-posed problem; Tikhonov regularization; Multi-parameter regularization
U2 - 10.1007/s10915-015-9990-x
DO - 10.1007/s10915-015-9990-x
M3 - Article
SN - 0885-7474
VL - 65
SP - 767
EP - 789
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
ER -