Algorithm 899: The Matlab postprocessing toolkit
ACM Transactions on Mathematical Software (TOMS)
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We propose a new strategy for choosing the optimal parameters for the Gegenbauer reconstruction method based on Chebyshev spectral coefficients under different assumptions on the smoothness of the function f. These parameters are optimal in the sense that the bounds on the truncation and regularization errors were forced to be equal. This strategy is independent on the number of terms N in the Chebyshev expansion of the function f and guarantees exponential convergence as $N\rightarrow \infty$ of the Gegenbauer series to f on the intervals of smoothness. The effectiveness of this strategy and exponential convergence are confirmed by numerical examples for functions with varying degrees of smoothness.