Geodesic
Approximate inversion of matrices in the process of solving a hypersingular integral equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 315-326

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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. 
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     author = {I. V. Oseledets and E. E. Tyrtyshnikov},
     title = {Approximate inversion of matrices in the process of solving a~hypersingular integral equation},
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I. V. Oseledets; E. E. Tyrtyshnikov. Approximate inversion of matrices in the process of solving a hypersingular integral equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 315-326. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a13/