A remark on solving large systems of equations in function spaces

I. Bremer; Klaus R. Schneider

Aplikace matematiky (1990)

  • Volume: 35, Issue: 6, page 494-498
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bremer, I., and Schneider, Klaus R.. "A remark on solving large systems of equations in function spaces." Aplikace matematiky 35.6 (1990): 494-498. <http://eudml.org/doc/15650>.

@article{Bremer1990,
abstract = {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.},
author = {Bremer, I., Schneider, Klaus R.},
journal = {Aplikace matematiky},
keywords = {large system; decomposition; block iterative algorithm; differential algebraic eqautions; splitting technique; partial orderings; nonlinear operator; complete metric space; fixed point equation; convergence; uniform contraction; splitting technique; partial orderings; nonlinear operator; complete metric space; system; fixed point equation; convergence; iterative procedure; uniform contraction},
language = {eng},
number = {6},
pages = {494-498},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on solving large systems of equations in function spaces},
url = {http://eudml.org/doc/15650},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Bremer, I.
AU - Schneider, Klaus R.
TI - A remark on solving large systems of equations in function spaces
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 6
SP - 494
EP - 498
AB - 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.
LA - eng
KW - large system; decomposition; block iterative algorithm; differential algebraic eqautions; splitting technique; partial orderings; nonlinear operator; complete metric space; fixed point equation; convergence; uniform contraction; splitting technique; partial orderings; nonlinear operator; complete metric space; system; fixed point equation; convergence; iterative procedure; uniform contraction
UR - http://eudml.org/doc/15650
ER -

References

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  1. G. Frobenius, Über Matrizen aus positiven Elementen, S. -B. Preuss. Akad. Wiss, Berlin 1908, 471-476, 1909, 514-518. (1908) 
  2. G. Frobenius, Über Matrizen aus nichtnegativen Elementen, S. -B. Preuss. Akad. Wiss. Berlin 1912, 456-477. (1912) 
  3. E. Lelarasmee A. E. Ruehli A. L. Sangiovanni- Vincentelli, 10.1109/TCAD.1982.1270004, IEEE Trans. CAD 1, (1982), 131-145. (1982) DOI10.1109/TCAD.1982.1270004
  4. A. R. Newton. A. L. Sangiovanni-Vincentelli, 10.1109/T-ED.1983.21275, IEEE Trans ED 30 (1983), 1184-1207. (1983) Zbl0526.65008DOI10.1109/T-ED.1983.21275
  5. J. M. Ortega W. C. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables, New York: Academic Press, 1970. (1970) MR0273810
  6. O. Perron, 10.1007/BF01449896, Math. Ann. 64 (1907), 248-263, (1907) MR1511438DOI10.1007/BF01449896
  7. K. R. Schneider, A remark on the waveform relaxation method, Int. J. Circuit Theory Appl. 18 (1990). (1990) 
  8. R. S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N. J. 1962. (1962) MR0158502

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