Tensor Approximation Approach to Calculation of Singular Values and Vectors for SVD Problem

A new method of calculation of singular values and left and right singular vectors of arbitrary nonsquare matrices is proposed. The method allows one to avoid solutions of high rank systems of linear equations of singular value decomposition problems, which makes it not sensitive to ill-conditioness of the decomposed matrix. On the base of the Eckart–Young theorem, it was shown that each second order r-rank tensor can be represented as a sum of the first rank r-order “coordinate” tensors. A new system of equations for “coordinate” tensor generator vectors was obtained. An iterative method of solution of the system was elaborated. Results of the method were compared with classical methods of solutions of singular value decomposition problems.