Block Power Method for SVD Decomposition

We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ R^n×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: A_k = U_k∑_kV_k^T , where ∑_k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ₁≥ σ₂ ⋯ ≥ σ_k. U_k and V_k are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.