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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
Summary:
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.
References:
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[2] Buchberger B., Emeljanenko G. A.: Methods of inversion of tridiagonal matrices. (Russian), Ž. Vyčisl. Mat. i Mat. Fiz., 13 (1973), 546-554. MR 0323799
[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 0276.34009
[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).
[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 0555861
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