Xu, Xiangjian A fast algorithm for solving a Toeplitz system. (English) Zbl 1298.65050 Appl. Math. Comput. 217, No. 5, 1944-1948 (2010). 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. Reviewer: Drahoslava Janovská (Praha) Cited in 1 ReviewCited in 2 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 15B05 Toeplitz, Cauchy, and related matrices Keywords:symmetric penta-diagonal systems of linear algebraic equations; fast direct algorithm for finding a solution; stability analysis; Toeplitz system; diagonally dominant; factorization PDFBibTeX XMLCite \textit{X. Xu}, Appl. Math. Comput. 217, No. 5, 1944--1948 (2010; Zbl 1298.65050) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.