Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Discrete least squares approximation by trigonometric polynomials


Authors: L. Reichel, G. S. Ammar and W. B. Gragg
Journal: Math. Comp. 57 (1991), 273-289
MSC: Primary 65D15
MathSciNet review: 1079030
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an efficient and reliable algorithm for discrete least squares approximation of a real-valued function given at arbitrary distinct nodes in $ [0,2\pi )$ by trigonometric polynomials. The algorithm is based on a scheme for the solution of an inverse eigenproblem for unitary Hessenberg matrices, and requires only $ O(mn)$ arithmetic operations as compared with $ O(m{n^2})$ operations needed for algorithms that ignore the structure of the problem. Moreover, the proposed algorithm produces consistently accurate results that are often better than those obtained by general QR decomposition methods for the least squares problem. Our algorithm can also be used for discrete least squares approximation on the unit circle by algebraic polynomials.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D15

Retrieve articles in all journals with MSC: 65D15


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1079030-8
PII: S 0025-5718(1991)1079030-8
Article copyright: © Copyright 1991 American Mathematical Society