An Algorithm for the Computation of the G-Singular Values of a Matrix

In this work we deal with the factorization A = UΣV + where Σ is a diagonal matrix, while U and V are orthogonal respect to the scalar product defined by the matrix G =diag(+1,−1, . . . ,−1), (the so-called Minkowski metric). This factorization is generalized requiring U and V to be orthogonal with respect to the scalar product defined by a generic diagonal matrix G =diag(±1). This factorization is called G−SVD, while the diagonal elements of Σ are called G−singular values. An iterative algorithm for the computation of the G−singular values is proposed and its convergence is also studied.