research-article

A class of first order factorization methods

Author:

Ivar GustafssonAuthors Info & Claims

Volume 18, Issue 2

Pages 142 - 156

https://doi.org/10.1007/BF01931691

Published: 01 June 1978 Publication History

Abstract

A class of first order factorization methods for the solution of large, symmetric, sparse systems of equations is introduced. Asymptotic results for the computational complexity are developed, results from numerical experiments are presented and comparisons with other iterative and direct methods are carried out.

References

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Axelsson OKohut RNeytcheva M(2023)An Implementation of a Coarse-Fine Mesh Stabilized Schwarz Method for a Three-Space Dimensional PDE-ProblemLarge-Scale Scientific Computations10.1007/978-3-031-56208-2_1(3-18)Online publication date: 5-Jun-2023
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Bai ZDuff IWathen A(2022)A Class of Incomplete Orthogonal Factorization Methods. I: Methods and TheoriesBIT10.1023/A:102191370069141:1(53-70)Online publication date: 11-Mar-2022
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A class of first order factorization methods

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Published In

BIT Volume 18, Issue 2

Jun 1978

116 pages

ISSN:0006-3835

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BIT Computer Science and Numerical Mathematics

United States

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Published: 01 June 1978

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Axelsson OKohut RNeytcheva M(2023)An Implementation of a Coarse-Fine Mesh Stabilized Schwarz Method for a Three-Space Dimensional PDE-ProblemLarge-Scale Scientific Computations10.1007/978-3-031-56208-2_1(3-18)Online publication date: 5-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-56208-2_1
Bai ZDuff IWathen A(2022)A Class of Incomplete Orthogonal Factorization Methods. I: Methods and TheoriesBIT10.1023/A:102191370069141:1(53-70)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1023/A%3A1021913700691
Brandén HSundqvist P(2022)Preconditioners Based on Fundamental SolutionsBIT10.1007/s10543-005-0010-745:3(481-494)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-005-0010-7
Bessonov OMeradji S(2021)Parallel modeling of wildfires using efficient solvers for ill-conditioned linear systemsThe Journal of Supercomputing10.1007/s11227-021-03632-877:9(9365-9379)Online publication date: 1-Sep-2021
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Chai MLuo KShao CWang HFan J(2020)A finite difference discretization method for heat and mass transfer with Robin boundary conditions on irregular domainsJournal of Computational Physics10.1016/j.jcp.2019.108890400:COnline publication date: 1-Jan-2020
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Axelsson O(2020)Extensions of a coarse–fine mesh stabilized Schwarz alternating iteration domain decomposition methodJournal of Computational and Applied Mathematics10.1016/j.cam.2019.112341364:COnline publication date: 15-Jan-2020
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Bebendorf MBollhöfer MBratsch M(2013)Hierarchical matrix approximation with blockwise constraintsBIT10.1007/s10543-012-0413-153:2(311-339)Online publication date: 1-Jun-2013
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Scott JTůma M(2011)The importance of structure in incomplete factorization preconditionersBIT10.1007/s10543-010-0299-851:2(385-404)Online publication date: 1-Jun-2011
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Cullum JTůma M(2006)Matrix-free preconditioning using partial matrix estimation BIT10.1007/s10543-006-0094-846:4(711-729)Online publication date: 1-Dec-2006
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Frank JVuik C(2001)On the Construction of Deflation-Based PreconditionersSIAM Journal on Scientific Computing10.1137/S106482750037323123:2(442-462)Online publication date: 1-Jan-2001
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Cited By

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Recommendations

On the Complexity of Sparse $QR$ and $LU$ Factorization of Finite-Element Matrices

Modified incomplete orthogonal factorization methods using Givens rotations

A Class of Incomplete Orthogonal Factorization Methods. I: Methods and Theories

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