@article{Zhang2023, 
author = {Xing Zhang and Xiaoyu Jiang and Zhaolin Jiang and Heejung Byun},
title = {Algorithms for solving a class of real quasi-symmetric Toeplitz linear systems and its applications},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {4},
pages = {1966-1981},
keywords = {image, encryption, decryption, decomposition, matrix inversion, quasi-symmetric Toeplitz matrix},
url = {https://www.sciopen.com/article/10.3934/era.2023101},
doi = {10.3934/era.2023101},
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.}
}