A Low Rank Tensorial Approximations method of computation of Singular Values and Singular Vectors for SVD problem

摘要

A new method of computation of singular values and left and right singular vectors of arbitrary non-square matrices has been proposed. The method permits to avoid solutions of high rank systems of linear equations of singular value decomposition problem, which makes it not sensitive to ill-conditioness of decomposed matrix. On base of Eckart-Young theorem, it was shown that each second order r-rank tensor can be represent as a sum of the first rank r-order "coordinate" tensors. A new system of equations for "coordinate" tensor's generators 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 problem.