TY - BOOK
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, eneralized 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, eneralized Lanczos bidiagonalization, generalized Krylov method, matrix pair decomposition, ill-posed problem, Tikhonov regularization, multi-parameter regularization.
M3 - Report
T3 - CASA-report
BT - A Golub-Kahan-type reduction method for matrix pairs
PB - Technische Universiteit Eindhoven
CY - Eindhoven
ER -