A Golub-Kahan-type reduction method for matrix pairs

M.E. Hochstenbach, L. Reichel, X. Yu

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)


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
Original languageEnglish
Pages (from-to)767-789
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - 2015


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