We consider a Vandermonde factorization of a Hankel matrix, and propose a new approach to compute the full decomposition in O(n2) operations. The method is based on the use of a variant of the Lanczos method to compute a tridiagonal matrix whose eigenvalues are the modes generating the entries in the Hankel matrix. By adapting existing methods to solve for these eigenvalues and then for the coefficients, one arrives at a method to compute the entire decomposition in O(n2) operations. The method is illustrated with a simple numerical example.
Bibliographical noteFunding Information:
author. E-mail: firstname.lastname@example.org. was partially supported by NSF Grants CCR-9405380 and CCR-9628786.
- Hankel matrix
- Lanczos algorithm
- Prony's method
- Vandermonde decomposition