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.

引用

页码：567 / 583

页数：17

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