| Title:
|
A remark on solving large systems of equations in function spaces (English) |
| Author:
|
Bremer, I. |
| Author:
|
Schneider, Klaus R. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
6 |
| Year:
|
1990 |
| Pages:
|
494-498 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems. (English) |
| Keyword:
|
large system |
| Keyword:
|
decomposition |
| Keyword:
|
block iterative algorithm |
| Keyword:
|
differential algebraic eqautions |
| Keyword:
|
splitting technique |
| Keyword:
|
partial orderings |
| Keyword:
|
nonlinear operator |
| Keyword:
|
complete metric space |
| Keyword:
|
fixed point equation |
| Keyword:
|
convergence |
| Keyword:
|
uniform contraction |
| MSC:
|
47H07 |
| MSC:
|
47J25 |
| MSC:
|
65H10 |
| MSC:
|
65J15 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0759.65033 |
| idMR:
|
MR1089930 |
| DOI:
|
10.21136/AM.1990.104432 |
| . |
| Date available:
|
2008-05-20T18:40:29Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104432 |
| . |
| Reference:
|
[1] G. Frobenius: Über Matrizen aus positiven Elementen.S. -B. Preuss. Akad. Wiss, Berlin 1908, 471-476, 1909, 514-518. |
| Reference:
|
[2] G. Frobenius: Über Matrizen aus nichtnegativen Elementen.S. -B. Preuss. Akad. Wiss. Berlin 1912, 456-477. |
| Reference:
|
[3] E. Lelarasmee A. E. Ruehli A. L. Sangiovanni- Vincentelli: The waveform relaxation method for the time domain analysis of large scale integrated circuits.IEEE Trans. CAD 1, (1982), 131-145. 10.1109/TCAD.1982.1270004 |
| Reference:
|
[4] A. R. Newton. A. L. Sangiovanni-Vincentelli: Relaxation based electrical simulation.IEEE Trans ED 30 (1983), 1184-1207. Zbl 0526.65008, 10.1109/T-ED.1983.21275 |
| Reference:
|
[5] J. M. Ortega W. C. Rheinboldt: Iterative Solutions of Nonlinear Equations in Several Variables.New York: Academic Press, 1970. MR 0273810 |
| Reference:
|
[6] O. Perron: Zur Theorie der Matrizen.Math. Ann. 64 (1907), 248-263, MR 1511438, 10.1007/BF01449896 |
| Reference:
|
[7] K. R. Schneider: A remark on the waveform relaxation method.Int. J. Circuit Theory Appl. 18 (1990). |
| Reference:
|
[8] R. S. Varga: Matrix iterative analysis.Prentice-Hall, Englewood Cliffs, N. J. 1962. MR 0158502 |
| . |
