Subspace iteration method for generalized singular values

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.