| Title:
|
On the choice of iteration parameters in the Stone incomplete factorization (English) |
| Author:
|
Segeth, Karel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
4 |
| Year:
|
1983 |
| Pages:
|
295-306 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Stone incomplete factorization |
| Keyword:
|
choice of parameters |
| Keyword:
|
Stone’s method |
| Keyword:
|
large sparse systems |
| Keyword:
|
Numerical experiments |
| MSC:
|
35J25 |
| MSC:
|
65F10 |
| MSC:
|
65F50 |
| MSC:
|
65N20 |
| MSC:
|
65N22 |
| idZBL:
|
Zbl 0532.65020 |
| idMR:
|
MR0710177 |
| DOI:
|
10.21136/AM.1983.104038 |
| . |
| Date available:
|
2008-05-20T18:22:44Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104038 |
| . |
| Reference:
|
[1] O. Axelsson: Solution of linear systems of equations: iterative methods. Sparse Matrix Techniques.(Advanced Course, Copenhagen 1976.) Lecture Notes in Mathematics, Vol. 572. Springer-Verlag, Berlin 1977, 1 - 51. MR 0448834 |
| Reference:
|
[2] I. Babuška M. Práger E. Vitásek: Numerical Processes in Differential Equations.SNTL7 Praha 1966. MR 0223101 |
| Reference:
|
[3] A. Bracha-Barak P. Saylor: A symmetric factorization procedure for the solution of elliptic boundary value problems.SIAM J. Numer. Anal. 10 (1973), 190-206. MR 0315876, 10.1137/0710020 |
| Reference:
|
[4] N. I. Buleev: A numerical method for solving two- and three-dimensional diffusion equations.(Russian.) Mat. Sb. 51 (1960), 227-238. |
| Reference:
|
[5] T. Dupont R. P. Kendall H. H. Rachford: An approximate factorization procedure for solving self-adjoint elliptic difference equations.SIAM J. Numer. Anal. 5 (1968), 559-573. MR 0235748, 10.1137/0705045 |
| Reference:
|
[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. |
| Reference:
|
[7] D. S. Kershaw: The incomplete Choleski-conjugate gradient method for iterative solution of systems of linear equations.J. Comput. Phys. 26 (1978), 43 - 65. MR 0488669, 10.1016/0021-9991(78)90098-0 |
| Reference:
|
[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. MR 0438681 |
| Reference:
|
[9] P. Saylor: Second order strongly implicit symmetric factorization methods for the solution of elliptic difference equations.SIAM J. Numer. Anal. 11 (1974), 894-908. Zbl 0295.65059, MR 0421105, 10.1137/0711071 |
| Reference:
|
[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. |
| Reference:
|
[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. MR 0790545 |
| Reference:
|
[12] S.Selberherr A.Schütz W. Petzl: MINIMOS - a two-dimensional MOS transistor singular analyser.IEEE J. Solid-State Circuits SC-15 (1980), 605-623. 10.1109/JSSC.1980.1051444 |
| Reference:
|
[13] H. L. Stone: Iterative solution of implicit approximations of multidimensional partial differential equations.SIAM J. Numer. Anal. 5 (1968), 530-558. Zbl 0197.13304, MR 0238504, 10.1137/0705044 |
| Reference:
|
[14] R. J. Taranto: Numerical studies of Stone's factorization and the iteration parameters, $\alpha$ and $\tau$.Rep. 423, Dept. of Computer Science, University of Illinois, Urbana, 111., 1971. |
| . |
