Preprints of the Keldysh Institute of Applied Mathematics
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Keldysh Institute preprints: Year: Volume: Issue: Page: Find

 Keldysh Institute preprints, 2013, 013, 17 pp. (Mi ipmp13)

Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix

I. E. Kaporin, O. Yu. Milyukova

Abstract: In the paper we consider the iterative solution of linear system $Ax=b$ by the conjugate gradient method using the factorized preconditioner $B=(I+LZ)Y(I+ZU)$, where $A=D+L+U$ is the additive splitting of the coefficient matrix into the strictly lower triangular, the diagonal, and the strictly upper triangular parts. For an arbitrary symmetric positive definite matrix $A$, the diagonal matrices $Y > 0$ and $Z$ are constructed as the minimizers of a certain upper bound for the K-condition number of the inverse preconditioned matrix. The main advantages of the new method are as follows: wide range of applicability, low operation number count per iteration, good parallelizability for all the stages of computation, and sufficient reduction of the iteration number (for a properly chosen preconditioning parameters). Numerical results are given for several test problems.

Keywords: onjugate gradient method, factorized preconditioner, the K-condition number

Full text: PDF file (391 kB)
Full text: http:/.../preprint.asp?id=2013-13&lg=r
References: PDF file   HTML file

Citation: I. E. Kaporin, O. Yu. Milyukova, “Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix”, Keldysh Institute preprints, 2013, 013, 17 pp.

Citation in format AMSBIB
\Bibitem{KapMil13} \by I.~E.~Kaporin, O.~Yu.~Milyukova \paper Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix \jour Keldysh Institute preprints \yr 2013 \papernumber 013 \totalpages 17 \mathnet{http://mi.mathnet.ru/ipmp13} 

• http://mi.mathnet.ru/eng/ipmp13
• http://mi.mathnet.ru/eng/ipmp/y2013/p13

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. O. Yu. Milyukova, “Parallelnye varianty metoda nepolnogo treugolnogo razlozheniya vtorogo poryadka sopryazhennykh gradientov na osnove ispolzovaniya spetsialnogo pereuporyadocheniya matritsy koeffitsientov”, Preprinty IPM im. M. V. Keldysha, 2014, 052, 32 pp.
2. O. Yu. Milyukova, “Sochetanie chislovykh i strukturnykh podkhodov k postroeniyu nepolnogo treugolnogo razlozheniya vtorogo poryadka v parallelnykh algoritmakh predobuslovlennogo metoda sopryazhennykh gradientov”, Preprinty IPM im. M. V. Keldysha, 2015, 010, 32 pp.
3. A. Gorobets, “On technology of large-scale CFD simulations”, Math. Models Comput. Simul., 8:6 (2016), 660–670
•  Number of views: This page: 292 Full text: 129 References: 18