Geodesic
On the existence of mosaic-skeleton approximations for discrete analogues of integral operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1421-1432

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Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described. 
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     author = {A. A. Kashirin and M. Yu. Taltykina},
     title = {On the existence of mosaic-skeleton approximations for discrete analogues of integral operators},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {57},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a1/}
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A. A. Kashirin; M. Yu. Taltykina. On the existence of mosaic-skeleton approximations for discrete analogues of integral operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1421-1432. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a1/