Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/62618
Título: | The eigen-structures of real (skew) circulant matrices with some applications |
Autor(es): | Liu, Zhongyun Chen, Siheng Xu, Weijin Zhang, Yulin |
Palavras-chave: | Real Schur form Real circulant matrices Real skew-circulant matrices CSCS iteration Real Toeplitz matrices |
Data: | 2019 |
Editora: | Springer Nature |
Revista: | Computational and Applied Mathematics |
Resumo(s): | The circulant matrices and skew-circulant matrices are two special classes of Toeplitz matrices and play vital roles in the computation of Toeplitz matrices. In this paper, we focus on real circulant and skew-circulant matrices. We first investigate their real Schur forms, which are closely related to the family of discrete cosine transform (DCT) and discrete sine transform (DST). Using those real Schur forms, we then develop some fast algorithms for computing real circulant, skew-circulant and Toeplitz matrix-real vector multiplications. Also, we develop a DCT-DST version of circulant and skew-circulant splitting (CSCS) iteration for real positive definite Toeplitz systems. Compared with the fast Fourier transform (FFT) version of CSCS iteration, the DCT-DST version is more efficient and saves a half storage. Numerical experiments are presented to illustrate the effectiveness of our method. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/62618 |
DOI: | 10.1007/s40314-019-0971-9 |
ISSN: | 2238-3603 |
e-ISSN: | 1807-0302 |
Versão da editora: | https://link.springer.com/article/10.1007/s40314-019-0971-9 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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real-cscs-final-zhang.pdf | 318,97 kB | Adobe PDF | Ver/Abrir |
Este trabalho está licenciado sob uma Licença Creative Commons