Previous |  Up |  Next


large system; decomposition; block iterative algorithm; differential algebraic eqautions; splitting technique; partial orderings; nonlinear operator; complete metric space; fixed point equation; convergence; uniform contraction
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.
[1] G. Frobenius: Über Matrizen aus positiven Elementen. S. -B. Preuss. Akad. Wiss, Berlin 1908, 471-476, 1909, 514-518.
[2] G. Frobenius: Über Matrizen aus nichtnegativen Elementen. S. -B. Preuss. Akad. Wiss. Berlin 1912, 456-477.
[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. DOI 10.1109/TCAD.1982.1270004
[4] A. R. Newton. A. L. Sangiovanni-Vincentelli: Relaxation based electrical simulation. IEEE Trans ED 30 (1983), 1184-1207. DOI 10.1109/T-ED.1983.21275 | Zbl 0526.65008
[5] J. M. Ortega W. C. Rheinboldt: Iterative Solutions of Nonlinear Equations in Several Variables. New York: Academic Press, 1970. MR 0273810
[6] O. Perron: Zur Theorie der Matrizen. Math. Ann. 64 (1907), 248-263, DOI 10.1007/BF01449896 | MR 1511438
[7] K. R. Schneider: A remark on the waveform relaxation method. Int. J. Circuit Theory Appl. 18 (1990).
[8] R. S. Varga: Matrix iterative analysis. Prentice-Hall, Englewood Cliffs, N. J. 1962. MR 0158502
Partner of
EuDML logo