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A fast algorithm for solving a Toeplitz system. (English) Zbl 1298.65050

The author derives a fast algorithm for solving symmetric penta-diagonal systems. The Toeplitz \(n \times n\) matrix \(A\) of the system of linear algebraic equations is decomposed. The Sherman-Morison-Woodbury formula is used to obtain conditions under which the matrix \(A\) is invertible. Quite complicated formulas lead to a fast algorithm for solving the original system. The author proves that for strictly diagonally dominant \(A\) the algorithm is stable and works well. Two numerical examples illustrate the theory.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
15B05 Toeplitz, Cauchy, and related matrices
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References:

[1] Nemani, S. S., A fast algorithm for solving Toeplitz penta-diagonal systems, Appl. Math. Comput., 215, 3830-3838 (2010) · Zbl 1194.65043
[2] Xu, Z.; An, X.; Lu, Q., A new modified algorithm for solving periodic Toeplitz tridiagonal systems, J. Numer. Methods Comput. Appl., 29, 291-295 (2008) · Zbl 1199.65086
[3] Nemani, S. S.; Garey, L. E., Parallel algorithms for solving tridiagonal and near-circulant system, Appl. Math. Comput., 130, 285-294 (2002) · Zbl 1038.65023
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