Approximate inversion of matrices in the process of solving a hypersingular integral equation

A method is proposed for approximate inversion of large matrices represented as sums of tensor products of smaller matrices. The method incorporates a modification, found by the authors, of the Newton–Hotelling–Schulz algorithm and uses a number of recently developed techniques for data compression and data structuring based on nonlinear approximations, such as tensor-product, low-rank, or wavelet approximations. The efficiency of the method is demonstrated with the help of matrices arising in the numerical solution of a hypersingular integral equation (namely, the Prandtl equation) on a square.