On singular values of Hankel operators of finite rank
By: William Gragg, Lother Reichel
Contributors: Reichel, Lother; Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1988
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 16
Subjects: OPERATORS(MATHEMATICS)
Other titles: NPS-53-89-003.
Description: 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.
Notes: Title from cover.

"NPS-53-89-003."

"November 1988."

AD A53-89-003.

Includes bibliographical references (p. 16).

aq/aq cc:9116 04/23/99.