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.
SIAM Journal on Numerical Analysis
Generalizing the GSVD.
SIAM Journal on Numerical Analysis,
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