Document Type


Publication Date



The generalized singular value decomposition (GSVD) of a pair of matrices is the natural tool for certain problems defined on Euclidean space, such as certain weighted least-squares problems, the result of applying Tikhonov regularization to such problems (sometimes called regularization with seminorms), and equality-constrained least-squares problems. There is an extension of the GSVD to pairs of bounded linear operators defined on Hilbert space that turns out to be a natural representation for analyzing the same problems in the infinite-dimensional setting.

Publisher's Statement

© 2016, Society for Industrial and Applied Mathematics. Article deposited here in compliance with publisher policy. Publisher's version of record:

Publication Title

SIAM Journal on Numerical Analysis


Publisher's PDF

Included in

Mathematics Commons