IKBFU's Vestnik

2015 Issue №10

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A method of an algorithm creation of cyclic reduction for solving of the system of equations with block-tridiagonal matrix

Pages
43-51

Abstract

An approach to the method of cyclic reduction for the system of equations with block-tridiagonal matrix of arbitrary dimension is presented. Formulas for elimination of unknowns in arbitrary order are obtained. Algorithms for the first and second boundary problems are described.

Reference

1. Buzbee B. L., Golub G. H., Nielson C. W. On direct methods for solving Poisson's equation // SIAM Journal of Numerical Analysis. 1970. № 7. P. 627–656.
2. Sweet R. A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimensions // SIAM J. Number. Anal. 1977. Vol. 14, № 4. P. 706-720.
3. Самарский А. А, Николаев Е. С. Методы решения сеточных уравнений. М., 1978.
4. Bank R. E., Rose D. J. Marching Algorithms For Elliptic Boundary Value Problems. The Constant Coefficient Case // SIAM J. Number. Anal. 1977. Vol. 14, № 5.