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Algorithms for solving a class of real quasi-symmetric Toeplitz linear systems and its applications.
- Source :
- Electronic Research Archive; 2023, Vol. 31 Issue 4, p1-16, 16p
- Publication Year :
- 2023
-
Abstract
- In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems with a constant symmetric Toeplitz matrix are solved. Second, two new fast algorithms are employed to solve the real quasi-symmetric Toeplitz linear system. Furthermore, we show a fast algorithm for quasi-symmetric Toeplitz matrix-vector multiplication. In addition, the stability analysis of the splitting symmetric Toeplitz inversion is discussed. In mathematical or engineering problems, the proposed algorithms are extraordinarily effective for solving a sequence of linear systems with a constant symmetric Toeplitz matrix. Fast matrix-vector multiplication and a quasi-symmetric Toeplitz linear solver are proven to be suitable for image encryption and decryption. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGORITHMS
TOEPLITZ matrices
LINEAR systems
MATHEMATICS
FACTORIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 26881594
- Volume :
- 31
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Electronic Research Archive
- Publication Type :
- Academic Journal
- Accession number :
- 178322075
- Full Text :
- https://doi.org/10.3934/era.2023101