Publicação
Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
| Resumo: | The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic. |
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| Autores principais: | Liu Zhongyun |
| Outros Autores: | Zhang Yulin; Ferreira, Carla; Ralha, Rui |
| Assunto: | Matrix square root Skew-Hamiltonian Schur decomposition Structure-preserving algorithm |
| Ano: | 2012 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic. |
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