Abstract
First we introduce a new class of highly differentiable generalized trigonometric polynomials. Then, we study some of their analytical properties, show that the computational effort for their utilization is similar to the one needed for ordinary trigonometric polynomials and discuss their superior performance in numerical experiments.
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References
C. W. Clenshaw,A note on the summation of Chebyshev series. Math. Tables & Aids to Computation,9, (1955), 118–120.
P. J. Davis,Interpolation and approximation, (1968). New York, Blaisdell.
C. Lanczos,Trigonometric interpolation of empirical and analytical functions. J. Math. Phys.,17, (1938), 123–199.
J. Lipka,Graphical and mechanical computation. (1918). London, J. Willey.
A. C. R. Newbery,Trigonometric interpolation and curve fitting, Mathematics of Computation,24, (1970), 869–876.
A. C. R. Newbery,A generalized interpolation algorithm. Math. Comp.,25, (1971), 549–552.
F. Oliveira-Pinto,Simultaneous trigonometric approximation of function and derivative. Comput. J.,16, (1973), 73–76.
F. Oliveira-Pinto,Generalized Chebyshev polynomials and their use in numerical approximation. Comput. J.,16, (1973), 375–379.
F. Oliveira-Pinto,Generalized Trigonometric Approximation, an outline. Estudos, (1974), Calouste Gulbenkian Foundation, Lisboa.
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Oliveira-Pinto, F. Experiments with a class of generalized trigonometric polynomials. Calcolo 21, 253–268 (1984). https://doi.org/10.1007/BF02576536
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DOI: https://doi.org/10.1007/BF02576536