Abstract

Abstract. We discuss a new method for the iterative computation of some of the generalized singular values and vectors of a large sparse matrix. Our starting point is the augmented matrix formulation of the GSVD. The subspace expansion is performed by (approximately) solving a Jacobi–Davidson type correction equation, while we give several alternatives for the subspace extraction. Numerical experiments indicate the efficiency of the method. Key words. Generalized singular value decomposition (GSVD), partial GSVD, Jacobi–Davidson, subspace method, augmented matrix, correction equation, (inexact) accelerated Newton, refined extraction, harmonic extraction. AMS subject classifications. 65F15, 65F50, (65F30). 1. Introduction. The generalized singular value decomposition (GSVD) was introduced by Van Loan [15] and further developed by Paige and Saunders [9]. Let A ∈ R m×n and B ∈ R p×n be given. The generalized singular values of the pair (A, B) are [15, Def. 1] Σ(A, B) = {σ ≥ 0 | A T A − σ 2 B T B singular}. The (diagonal form of the) GSVD of A and B is given by [15, Th. 2], [9, p. 399]

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