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EnglishDespite the fact that symmetric Toeplitz matrices can have arbitrary eigenvalues, the numerical construction of such a matrix having prescribed eigenvalues remains to be a challenge. A two-step method using the continuation idea is proposed in this paper. The first step constructs a centro-symmetric Jacobi matrix with the prescribed eigenvalues in finitely many steps. The second step uses the Cayley transform to integrate flows in the linear subspace of skew-symmetric and centro-symmetric matrices. No special geometric integrators are needed. The convergence analysis is illustrated for the case of n = 3. Numerical examples are presented.
| Titolo: | “The Cayley Method and the Inverse Eigenvalue Problem for Toeplitz Matrices” |
| Autori: | |
| Data di pubblicazione: | 2002 |
| Rivista: | |
| Abstract: | Despite the fact that symmetric Toeplitz matrices can have arbitrary eigenvalues, the numerical construction of such a matrix having prescribed eigenvalues remains to be a challenge. A two-step method using the continuation idea is proposed in this paper. The first step constructs a centro-symmetric Jacobi matrix with the prescribed eigenvalues in finitely many steps. The second step uses the Cayley transform to integrate flows in the linear subspace of skew-symmetric and centro-symmetric matrices. No special geometric integrators are needed. The convergence analysis is illustrated for the case of n = 3. Numerical examples are presented. |
| Handle: | http://hdl.handle.net/11587/103724 |
| Appare nelle tipologie: | Articolo pubblicato su Rivista |
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