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Speaker: Jake Roberts, MTU;

Abstract:

The generalized singular value decomposition (GSVD) of a pair of matrices is a commonly used tool for many problems that take place in Euclidean space, such as weighted least-squares problems that arise from Tikhonov regularization. There is an extension of the GSVD to pairs of operators defined on a Hilbert space that we call the generalized singular value expansion (GSVE) of a pair of operators. If we consider a pair of operators T and L, we are able to construct a sequence of finite rank operators Tn and Ln that converge to T and L. When looking at the GSVD of the matrix forms for Tn and Ln, we are able to analyze the GSVE of the pair of operators T and L.