Subspace iteration method for generalized singular values

Abstract

It's well known that the Singular Values Decomposition (SVD) is useful in
many applications such as low rank approximation, data reductions,
identification of the best approximation of the original data points using
fewer dimensions. It's also a useful tool for computation of eigenvalues of
matrix $A^{T}A$ without  explicitly forming the matrix product. The Generalized
Singular Values Decomposition (GSVD) of the pair $(A,B)$ is also a useful tool for
computation of the generalized eigenvalues of the symmetric pencil $%
A^{T}A-\lambda B^{T}B$. The generalized singular values of the pair $(A,B)$
are nothing but the square roots of generalized eigenvalues of the symmetric
eigenproblem $A^{T}Av-\lambda B^{T}Bv=0$. The novelty of this work is the method that
computes the largest generalized singular values and vectors using iterative
subspace-like method.