Fast algorithms for perturbed Toeplitz-plus-Hankel system based on discrete cosine transform and their applications

被引：8
|
作者：
Zhang, Xing [1 ,2 ]
Zheng, Yanpeng [3 ]
Jiang, Zhaolin [4 ]
Byun, Heejung [2 ]
机构：
[1] Linyi Univ, Sch Informat Sci & Technol, Linyi 276000, Peoples R China
[2] Univ Suwon, Coll Informat Technol, Hwaseong Si 445743, South Korea
[3] Linyi Univ, Sch Automat & Elect Engn, Linyi 276000, Shandong, Peoples R China
[4] Linyi Univ, Sch Math & Stat, Linyi 276000, Peoples R China
来源：
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2024年 / 41卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fast algorithm; Toeplitz-plus-Hankel system; Symmetric centrosymmetric matrix; Discrete cosine transform; MATRICES;
D O I：
10.1007/s13160-023-00616-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A class of perturbed Toeplitz-plus-Hankel matrices are studied in this paper. Firstly, we present two fast algorithms for computing the eigenvalues of a Toeplitz-plus-Hankel matrix which can be diagonalized by discrete cosine transform. Based on the diagonalization of the Toeplitz-plus-Hankel matrix, algorithms for fast Toeplitz-plus-Hankel matrix-vector multiplication and solving the Toeplitz-plus-Hankel system are given. Secondly, we propose two new algorithms with less computational time to solve the perturbed Toeplitz-plus-Hankel linear system. Thirdly, image encryption and decryption utilizing the proposed algorithms are shown. Finally, the effectiveness of our proposed algorithms is verified by numerical experiments.
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页码：567 / 583
页数：17
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