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Fast algorithms for perturbed Toeplitz-plus-Hankel system based on discrete cosine transform and their applications
Ist Teil von
Japan journal of industrial and applied mathematics, 2024, Vol.41 (1), p.567-583
Ort / Verlag
Tokyo: Springer Japan
Erscheinungsjahr
2024
Link zum Volltext
Quelle
SpringerLink (Online service)
Beschreibungen/Notizen
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.