Downdating of Szego polynomials and data fitting applications
By: W.B. Gragg, G.S. Ammar, L. Reichel
Contributors: Ammar, Gregory  S.; Reichel, Lother; Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1992
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 18
Subjects: Fitting functions(Mathematics); Algorithms; Polynomials
Other titles: NPS-MA-92-002.
Description: Many algorithms for polynomial least squares approximation of real- valued function on a      real interval determine polynomials that are orthogonal with respect to a suitable inner      product defined on this interval. Analogously, it is convenient to computer Szego      polynomials, i.e., polynomials that are orthogonal with respect to an inner product on the      unit circle, when approximating a complex-valued function on the unit circle in the least      squares sense. It may also be appropriate to determine Szego polynomials in algorithms      for least squares approximation of real-valued periodic functions by trigonometric      polynomials. This paper is concerned with Szego polynomials that are defined by a      discrete inner product on the unit circle. We present a scheme for downdating the Szego      polynomials and given least squares approximant when a node is deleted from the inner      product. Our scheme uses the QR algorithm for unitary upper IIessenberg matrices. We      describe a data-fitting application that illustrates how our scheme can be combined with      the fast Fourier transform algorithm when the given nodes are not equidistant. Application      to sliding windows is discussed also.
Notes: Title from cover.

"NPS-MA-92-002."

"January 1992."

AD A245 825.

Includes bibliographical references (p. 18).

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