### Abstract

The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n^{2} is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

Original language | English (US) |
---|---|

Pages (from-to) | 245-258 |

Number of pages | 14 |

Journal | Computing (Vienna/New York) |

Volume | 58 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computing (Vienna/New York)*,

*58*(3), 245-258. https://doi.org/10.1007/BF02684392

}

*Computing (Vienna/New York)*, vol. 58, no. 3, pp. 245-258. https://doi.org/10.1007/BF02684392

**Circulant block-factorization preconditioning of anisotropic elliptic problems.** / Lirkov, I. D.; Margenov, S. D.; Zikatanov, Ludmil Tomov.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Circulant block-factorization preconditioning of anisotropic elliptic problems

AU - Lirkov, I. D.

AU - Margenov, S. D.

AU - Zikatanov, Ludmil Tomov

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n2 is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

AB - The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n2 is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

UR - http://www.scopus.com/inward/record.url?scp=0030662736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030662736&partnerID=8YFLogxK

U2 - 10.1007/BF02684392

DO - 10.1007/BF02684392

M3 - Article

AN - SCOPUS:0030662736

VL - 58

SP - 245

EP - 258

JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

SN - 0010-485X

IS - 3

ER -