Publication:
On singular values of Hankel operators of finite rank

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Authors
Gragg, William B.
Reichel, Lother
Subjects
Hankel operator
singular values
generalized Takagi singular value problem
generalized eigenvalue problem, Lanczos iterations
Advisors
Date of Issue
1988-11
Date
1988-11
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
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
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-53-89-003
Sponsors
Naval Postgraduate School and the National Science Foundation , Washington D.C.
Funder
O&MN, Direct funding
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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