General theory of direct methods for solving systems of equations with band matrices
Applications of Mathematics, Tome 24 (1979) no. 3, pp. 161-183
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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.
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.
DOI : 10.21136/AM.1979.103794
Classification : 65F05, 65F30
Keywords: general theory of direct methods; band matrices; factorization methods; Gaussian elimination; transfer of the boundary condition
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Malina, Ľubor. General theory of direct methods for solving systems of equations with band matrices. Applications of Mathematics, Tome 24 (1979) no. 3, pp. 161-183. doi: 10.21136/AM.1979.103794

[1] Babuška I., Práger M., Vitásek E.: Numerical processes in differential equations. Interscience, New York (1966). | MR

[2] Buchberger B., Emeljanenko G. A.: Methods of inversion of tridiagonal matrices. (Russian), Ž. Vyčisl. Mat. i Mat. Fiz., 13 (1973), 546-554. | MR

[3] Samarskij A. A.: Introduction into the theory of difference methods. (Russian), Moscow (1971).

[4] Taufer J.: Lösung der Randwertprobleme für Systeme von Linearen Differentialgleichungen. Rozpravy ČSAV, 83 (1973). | Zbl

[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).

[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. | MR

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