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The generalized singular value expansion (GSVE) simultaneously diagonalizes a pair of operators on Hilbert space. From a theoretical point of view, the GSVE enables a straightforward analysis of, for example, weighted least-squares problems and the method of Tikhonov regularization with seminorms. When the operators are discretized, an approximate GSVE can be computed from the generalized singular value decomposition of a pair of Galerkin matrices. Unless the discretization is carefully chosen, spurious modes can appear, but a natural condition on the discretization guarantees convergence of the approximate GSVE to the exact one. Numerical examples illustrate the pitfalls of a poor discretization and efficacy of the convergence conditions.

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Copyright 2018 Society for Industrial and Applied Mathematics. Article deposited here in compliance with publisher policy. Publisher's version of record:

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SIAM Journal on Numerical Analysis


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