TITLE:
Alternative Fourier Series Expansions with Accelerated Convergence
AUTHORS:
Wenlong Li
KEYWORDS:
Fourier Series, Trigonometric Series, Fourier Approximation, Convergence Acceleration
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.15,
September
23,
2016
ABSTRACT: The key objective of this paper is to
improve the approximation of a sufficiently smooth nonperiodic function defined
on a compact interval by proposing alternative forms of Fourier series
expansions. Unlike in classical Fourier series, the expansion coefficients
herein are explicitly dependent not only on the function itself, but also on
its derivatives at the ends of the interval. Each of these series expansions
can be made to converge faster at a desired polynomial rate. These results have
useful implications to Fourier or harmonic analysis, solutions to differential
equations and boundary value problems, data compression, and so on.