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direct methods; band matrices; Gauss-Jordan elimination; numerical stability; algorithms; well conditioned systems; fast Fourier technique
The methods of the transfer of conditions are generalized so that they also cover the direct methods leading to the diagonalization of the original matrix of a system with a band matrix. Part 3 is devoted to the numerical stability of methods of the transfer of conditions described in author's previous paper. Finally, it is shown how to obtain a particular method by the choice parameters of the general algorithm.
[1] Godunov S. K., Rjabenkij V. S.: Difference schemes. (Russian) Nauka, Moscow (1973).
[2] Malina Ľ.: General theory of direct methods for solving systems of equations with band matrices. (To appear in Aplikace matematiky). Zbl 0443.65011
[3] 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
[4] Taufer J.: Lösung der Randwertprobleme für Systeme von Linearen Differentialgleichungen. Rozpravy ČSAV, 83 (1973). Zbl 0276.34009
[5] Hockney R. W.: A fast direct solution of Poisson's equation using Fourrier analysis. J. of Association for Computing Machinery, 12 (1965), 95-113. DOI 10.1145/321250.321259 | MR 0213048
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