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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

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Volume 19, Issue 1

# Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain

Ekaterina A. Muravleva
• Corresponding author
• Skolkovo Institute of Science and Technology, Skolkovo Innovation Center Moscow, 143025, Nobel St. 3, Moscow, Russia
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• Other articles by this author:
• De Gruyter OnlineGoogle Scholar
/ Ivan V. Oseledets
• Skolkovo Institute of Science and Technology, Skolkovo Innovation Center Moscow, 143025, Nobel St. 3, Moscow, Russia
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• Other articles by this author:
• De Gruyter OnlineGoogle Scholar
Published Online: 2018-07-21 | DOI: https://doi.org/10.1515/cmam-2018-0026

## Abstract

In this paper we propose an efficient algorithm to compute low-rank approximation to the solution of so-called “Laplace-like” linear systems. The idea is to transform the problem into the frequency domain, and then use cross approximation. In this case, we do not need to form explicit approximation to the inverse operator, and can approximate the solution directly, which leads to reduced complexity. We demonstrate that our method is fast and robust by using it as a solver inside Uzawa iterative method for solving the Stokes problem.

MSC 2010: 65F10; 15A09

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## About the article

Revised: 2018-02-02

Accepted: 2018-05-02

Published Online: 2018-07-21

Published in Print: 2019-01-01

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 16-31-60095

This work was supported by the Russian Foundation for Basic Research, grant 16-31-60095.

Citation Information: Computational Methods in Applied Mathematics, Volume 19, Issue 1, Pages 137–145, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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