On Singular Values of Hankel Operators of Finite Rank
Abstract
Let H be a Hankel operator defined by its symbol rho = pi X Chi where is a monic polynomial of degree n and pi is a polynomial of degree less than n. Then H has rank n. We derive a generalized Takagi singular value problem defined by two n x n matrices, such that its n generalized Takagi singular values are the positive singular values of H. If rho is real, then the generalized Takagi singular value problem reduces to a generalized symmetric eigenvalue problem. The computations can be carried out so that the Lanczos method applied to the latter problem requires only 0(n log n) arithmetic operations for each iteration. If pi and chi are given in power form, then the elements of all n x n matrices required can be determined in 0(sq.n) arithmetic operations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1988
- Accession Number
- ADA204163
Entities
People
- Lother Reichel
- William Gragg
Organizations
- Naval Postgraduate School