Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Rational trigonometric approximations using Fourier series partial sums
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
On a Rational Linear Approximation of Fourier Series for Smooth Functions
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Recovering Exponential Accuracy from Non-harmonic Fourier Data Through Spectral Reprojection
Journal of Scientific Computing
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A family of simple, periodic basis functions with “built-in” discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representation of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.