Block Power Method for SVD Decomposition
Abdeslem Hafid Bentbib, Ahmed Kanber · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · 2015
Abstract 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 ∑ k V k T , where ∑ k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ 1 ≥ σ 2 ⋯ ≥ 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.