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An efficient numerical algorithm for solving linear systems with cyclic tridiagonal coefficient matrices.
- Source :
-
Journal of Mathematical Chemistry . Sep2024, Vol. 62 Issue 8, p1808-1821. 14p. - Publication Year :
- 2024
-
Abstract
- In the present paper, we mainly consider the direct solution of cyclic tridiagonal linear systems. By using the specific low-rank and Toeplitz-like structure, we derive a structure-preserving factorization of the coefficient matrix. Based on the combination of such matrix factorization and Sherman–Morrison–Woodbury formula, we then propose a cost-efficient algorithm for numerically solving cyclic tridiagonal linear systems, which requires less memory storage and data transmission. Furthermore, we show that the structure-preserving matrix factorization can provide us with an explicit formula for n-th order cyclic tridiagonal determinants. Numerical examples are given to demonstrate the performance and efficiency of our algorithm. All of the experiments are performed on a computer with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02599791
- Volume :
- 62
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Chemistry
- Publication Type :
- Academic Journal
- Accession number :
- 178878133
- Full Text :
- https://doi.org/10.1007/s10910-024-01631-7