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 -