On the choice of iteration parameters in the Stone incomplete factorization

Karel Segeth

Aplikace matematiky (1983)

  • Volume: 28, Issue: 4, page 295-306
  • ISSN: 0862-7940

Abstract

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The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved.

How to cite

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Segeth, Karel. "On the choice of iteration parameters in the Stone incomplete factorization." Aplikace matematiky 28.4 (1983): 295-306. <http://eudml.org/doc/15307>.

@article{Segeth1983,
abstract = {The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved.},
author = {Segeth, Karel},
journal = {Aplikace matematiky},
keywords = {Stone incomplete factorization; choice of parameters; Stone’s method; large sparse systems; Numerical experiments; Stone incomplete factorization; choice of parameters; Stone's method; large sparse systems; Numerical experiments},
language = {eng},
number = {4},
pages = {295-306},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the choice of iteration parameters in the Stone incomplete factorization},
url = {http://eudml.org/doc/15307},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Segeth, Karel
TI - On the choice of iteration parameters in the Stone incomplete factorization
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 4
SP - 295
EP - 306
AB - The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved.
LA - eng
KW - Stone incomplete factorization; choice of parameters; Stone’s method; large sparse systems; Numerical experiments; Stone incomplete factorization; choice of parameters; Stone's method; large sparse systems; Numerical experiments
UR - http://eudml.org/doc/15307
ER -

References

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  2. I. Babuška M. Práger E. Vitásek, Numerical Processes in Differential Equations, SNTL7 Praha 1966. (1966) MR0223101
  3. A. Bracha-Barak P. Saylor, 10.1137/0710020, SIAM J. Numer. Anal. 10 (1973), 190-206. (1973) MR0315876DOI10.1137/0710020
  4. N. I. Buleev, A numerical method for solving two- and three-dimensional diffusion equations, (Russian.) Mat. Sb. 51 (1960), 227-238. (1960) 
  5. T. Dupont R. P. Kendall H. H. Rachford, 10.1137/0705045, SIAM J. Numer. Anal. 5 (1968), 559-573. (1968) MR0235748DOI10.1137/0705045
  6. I. Gustafsson, On first and second order symmetric factorization methods for the solution of elliptic difference equations, Res. Rep. 78.01 R, Dept. of Computer Sciences, Chalmers University of Technology and the University of Goteborg, Goteborg 1978. (1978) 
  7. D. S. Kershaw, 10.1016/0021-9991(78)90098-0, J. Comput. Phys. 26 (1978), 43 - 65. (1978) MR0488669DOI10.1016/0021-9991(78)90098-0
  8. J. A. Meijerink H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Соmр. 31 (1977), 148-162. (1977) MR0438681
  9. P. Saylor, 10.1137/0711071, SIAM J. Numer. Anal. 11 (1974), 894-908. (1974) Zbl0295.65059MR0421105DOI10.1137/0711071
  10. K. Segeth, The iterative use of fast algorithms for the solution of elliptic partial differential equations, (Lecture at the summer school Software a algoritmy numerické matematiky 4, Karlovy Vary 1981.) Matematický ústav ČSAV, Praha 1983. (1981) 
  11. K. Segeth, Numerical experiments with the Stone incomplete triangular decomposition, Mathematical Models in Physics and Chemistry and Their Numerical Realization 3. (School-Seminar, Visegrád 1982.) To appear. (1982) MR0790545
  12. S.Selberherr A.Schütz W. Petzl, 10.1109/JSSC.1980.1051444, IEEE J. Solid-State Circuits SC-15 (1980), 605-623. (1980) DOI10.1109/JSSC.1980.1051444
  13. H. L. Stone, 10.1137/0705044, SIAM J. Numer. Anal. 5 (1968), 530-558. (1968) Zbl0197.13304MR0238504DOI10.1137/0705044
  14. R. J. Taranto, Numerical studies of Stone’s factorization and the iteration parameters, α and τ , Rep. 423, Dept. of Computer Science, University of Illinois, Urbana, 111., 1971. (1971) 

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