Abstract
In this paper, we consider the matrices approximated in \({\mathscr{H}}^{2}\) format. The direct solution, as well as the preconditioning of systems with such matrices, is a challenging problem. We propose a non-extensive sparse factorization of the \({\mathscr{H}}^{2}\) matrix that allows to substitute direct \({\mathscr{H}}^{2}\) solution with the solution of the system with an equivalent sparse matrix of the same size. The sparse factorization is constructed of parameters of the \({\mathscr{H}}^{2}\) matrix. In the numerical experiments, we show the consistency of this approach in comparison with the other approximate block low-rank hierarchical solvers, such as HODLR [3], H2Lib [5], and IFMM [11].
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Section 2 is supported by Russian Foundation for Basic Research grant 17-01-00854, Sections 3 and 4 are supported by Russian Foundation for Basic Research grant 16-31-60095, Sectiom 5 is supported by Russian Science Foundation grant 15-11-00033.
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Communicated by: Leslie Greengard
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Sushnikova, D.A., Oseledets, I.V. Simple non-extensive sparsification of the hierarchical matrices. Adv Comput Math 46, 52 (2020). https://doi.org/10.1007/s10444-020-09794-y
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DOI: https://doi.org/10.1007/s10444-020-09794-y