| Journal: | Computational & applied mathematics |
| Database: | PERIÓDICA |
| System number: | 000269390 |
| ISSN: | 1807-0302 |
| Authors: | Bazan, Fermin S. Viloche1 |
| Institutions: | 1Universidade Federal de Santa Catarina, Departamento de Matematica, Florianopolis, Santa Catarina. Brasil |
| Year: | 2005 |
| Season: | Sep-Dic |
| Volumen: | 24 |
| Number: | 3 |
| Pages: | 365-392 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico, descriptivo |
| English abstract | Let Pm(z) be a matrix polynomial of degree m whose coefficients At Î Cq×q satisfy a recurrence relation of the form: hkA0+ hk+1A1+...+ hk+m-1Am-1 = hk+m, k > 0, where hk = RZkL Î Cp×q, R Î Cp×n, Z = diag (z1,...,zn) with zi ¹ zj for i ¹ j, 0 < |zj| < 1, and L Î Cn×q. The coefficients are not uniquely determined from the recurrence relation but the polynomials are always guaranteed to have n fixed eigenpairs, {zj,lj}, where lj is the jth column of L*. In this paper, we show that the zj's are also the n eigenvalues of an n×n matrix CA; based on this result the sensitivity of the zj's is investigated and bounds for their condition numbers are provided. The main result is that the zj's become relatively insensitive to perturbations in CA provided that the polynomial degree is large enough, the number n is small, and the eigenvalues are close to the unit circle but not extremely close to each other. Numerical results corresponding to a matrix polynomial arising from an application in system theory show that low sensitivity is possible even if the spectrum presents clustered eigenvalues |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas aplicadas, Matrices polinominales, Eigenvalores |
| Keyword: | Mathematics, Applied mathematics, Matrix polynomials, Eigenvalues |
| Full text: | Texto completo (Ver HTML) |
