General theory of direct methods for solving systems of equations with band matrices

Ľubor Malina

Aplikace matematiky (1979)

  • Volume: 24, Issue: 3, page 161-183
  • ISSN: 0862-7940

Abstract

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A unified approach to the theory and construction of direct methods is presented. The approach is based on the idea of the transfer of conditions. In examples it is shown how to obtain a particular method from the general algorithm.

How to cite

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Malina, Ľubor. "General theory of direct methods for solving systems of equations with band matrices." Aplikace matematiky 24.3 (1979): 161-183. <http://eudml.org/doc/15092>.

@article{Malina1979,
abstract = {A unified approach to the theory and construction of direct methods is presented. The approach is based on the idea of the transfer of conditions. In examples it is shown how to obtain a particular method from the general algorithm.},
author = {Malina, Ľubor},
journal = {Aplikace matematiky},
keywords = {general theory of direct methods; band matrices; factorization methods; Gaussian elimination; transfer of the boundary condition; general theory of direct methods; band matrices; factorization methods; Gaussian elimination; transfer of the boundary condition},
language = {eng},
number = {3},
pages = {161-183},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {General theory of direct methods for solving systems of equations with band matrices},
url = {http://eudml.org/doc/15092},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Malina, Ľubor
TI - General theory of direct methods for solving systems of equations with band matrices
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 3
SP - 161
EP - 183
AB - A unified approach to the theory and construction of direct methods is presented. The approach is based on the idea of the transfer of conditions. In examples it is shown how to obtain a particular method from the general algorithm.
LA - eng
KW - general theory of direct methods; band matrices; factorization methods; Gaussian elimination; transfer of the boundary condition; general theory of direct methods; band matrices; factorization methods; Gaussian elimination; transfer of the boundary condition
UR - http://eudml.org/doc/15092
ER -

References

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  1. Babuška I., Práger M., Vitásek E., Numerical processes in differential equations, Interscience, New York (1966). (1966) MR0223101
  2. Buchberger B., Emeljanenko G. A., Methods of inversion of tridiagonal matrices, (Russian), Ž. Vyčisl. Mat. i Mat. Fiz., 13 (1973), 546-554. (1973) MR0323799
  3. Samarskij A. A., Introduction into the theory of difference methods, (Russian), Moscow (1971). (1971) 
  4. Taufer J., Lösung der Randwertprobleme für Systeme von Linearen Differentialgleichungen, Rozpravy ČSAV, 83 (1973). (1973) Zbl0276.34009
  5. Ting C. T. Т., A method of solving a system of linear equations whose coefficients form a tridiagonal matrix, Quart. of Appl. Maths., XXII (1962). (1962) 
  6. Malina Ľ., Methods of the transfer of conditions and conditions of "well conditionedness", (Russian), in Numerical methods of linear algebra, ed. G. I. Marčuk, Novosibirsk (1977), 87-96. (1977) MR0555861

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