Simple non-extensive sparsification of the hierarchical matrices

Daria A. Sushnikova; Ivan V. Oseledets

doi:10.1007/s10444-020-09794-y

Simple non-extensive sparsification of the hierarchical matrices

Daria A. Sushnikova^*, Ivan V. Oseledets

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider the matrices approximated in 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 H 2 matrix that allows to substitute direct 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 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].

Original language	English (US)
Article number	52
Journal	Advances in Computational Mathematics
Volume	46
Issue number	4
DOIs	https://doi.org/10.1007/s10444-020-09794-y
State	Published - Jul 1 2020

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

H matrix
Preconditioning
Sparse factorization

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s10444-020-09794-y

Cite this

@article{f82f0f8bf5cd48f1bf14afe9b83657f1,

title = "Simple non-extensive sparsification of the hierarchical matrices",

abstract = "In this paper, we consider the matrices approximated in 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 H 2 matrix that allows to substitute direct 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 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].",

keywords = "H matrix, Preconditioning, Sparse factorization",

author = "Sushnikova, {Daria A.} and Oseledets, {Ivan V.}",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = jul,

day = "1",

doi = "10.1007/s10444-020-09794-y",

language = "English (US)",

volume = "46",

journal = "Advances in Computational Mathematics",

issn = "1019-7168",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - Simple non-extensive sparsification of the hierarchical matrices

AU - Sushnikova, Daria A.

AU - Oseledets, Ivan V.

N1 - Funding Information: 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. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - In this paper, we consider the matrices approximated in 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 H 2 matrix that allows to substitute direct 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 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].

AB - In this paper, we consider the matrices approximated in 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 H 2 matrix that allows to substitute direct 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 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].

KW - H matrix

KW - Preconditioning

KW - Sparse factorization

UR - http://www.scopus.com/inward/record.url?scp=85088709758&partnerID=8YFLogxK

U2 - 10.1007/s10444-020-09794-y

DO - 10.1007/s10444-020-09794-y

M3 - Article

AN - SCOPUS:85088709758

SN - 1019-7168

VL - 46

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 4

M1 - 52

ER -

Simple non-extensive sparsification of the hierarchical matrices

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this