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2010

On the Fourier Extension of Nonperiodic Functions

8 years 5 months ago
On the Fourier Extension of Nonperiodic Functions
We obtain exponentially accurate Fourier series for nonperiodic functions on the interval [-1, 1] by extending these functions to periodic functions on a larger domain. The series may be evaluated, but not constructed, by means of the FFT. A complete convergence theory is given based on orthogonal polynomials that resemble Chebyshev polynomials of the first and second kinds. We analyze a previously proposed numerical method, which is unstable in theory but stable in practice. We propose a new numerical method that is stable both in theory and in practice. Key words. Fourier series, orthogonal polynomials, least squares, frames AMS subject classifications. 42A10, 42C15, 65T40 DOI. 10.1137/090752456
Daan Huybrechs
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMNUM
Authors Daan Huybrechs
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