Volume 4, pp. 64-74, 1996.
A note on Newbery's algorithm for discrete least-squares approximation by trigonometric polynomials
Heike Faßbender
Abstract
Recently fast, efficient and reliable algorithms for discrete least-squares
approximation of a real-valued function given at arbitrary distinct nodes in
by trigonometric polynomials were presented in different papers.
These algorithms are based on schemes for the solution of inverse unitary
eigenproblems and require only O() arithmetic operations as compared to
O() operations needed for algorithms that ignore the structure of the
problem. In 1970 Newbery already presented a O() algorithm for solving the
discrete least-squares approximation by trigonometric polynomials. In
this paper the connection between the different algorithms is illustrated.
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Key words
trigonometric approximation.
AMS subject classifications
65D10, 42A10, 65F99.