A strategy for choosing Gegenbauer reconstruction parameters for numerical stability

Jackiewicz, Zdzisław; Park, R.

doi:10.1016/j.amc.2009.02.034

Cited by 3 publications

(6 citation statements)

References 18 publications

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“…3 by contour plots of q T (α, N, m) N given by (3.2) for m = 6. Here we note that the analytical determination of α opt , which in turn successfully predicted the corresponding numerical results, is a welcome improvement over the nature of the problem in [20] where β opt could only be determined numerically.…”

Section: Behavior Of Error Bounds For the Gegenbauer Methods In Applicmentioning

confidence: 99%

“…Our last study demonstrated how asymptotic analysis could be used to find the Chebyshev-Gegenbauer reconstruction parameters best suited for avoiding numerical instability [20]. In this paper we again use asymptotic analysis as a method for locating optimal parameters for a Chebyshev-Gegenbauer reconstruction.…”

Section: Introductionmentioning

confidence: 99%

“…Previous studies, such as [2,3,20] have shown the effectiveness of performing Gegenbauer reconstructions on two-dimensional images, defined, of course, on evenly spaced grid points. In such cases the source data was understood to be from frequency space and hence, one-dimensional Fourier-Gegenbauer reconstructions were performed on each vertical column, or horizontal row, of data.…”

Section: Two-dimensional Reconstructionmentioning

confidence: 99%

“…As we shall see, such minimal values of error will likely be acceptable for many practical applications. Finally, we recognize that there are a significant number of symbols in this study and thus refer the reader to the symbol table in our last paper, [20].…”

Section: Background and Notationmentioning

confidence: 99%

“…Here however we have modified the constraint so that the optimal parameters will be useful to applications seeking to either bound the number of Gegenbauer expansion coefficients or to control compression ratios. Also, unlike the approach used in [20], which could only be determined numerically, here we will be able to predict the solutions analytically prior to demonstrating them numerically.…”

Section: Introductionmentioning

confidence: 99%

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A New Strategy for Choosing the Chebyshev‐gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis

Jackiewicz

Park

2010

Mathematical Modelling and Analysis

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Abstract. The Gegenbauer reconstruction method, first proposed by Gottlieb et.al. in 1992, has been considered a useful technique for re-expanding finite series polynomial approximations while simultaneously avoiding Gibbs artifacts. Since its introduction many studies have analyzed the method's strengths and weaknesses as well as suggesting several applications. However, until recently no attempts were made to optimize the reconstruction parameters, whose careful selection can make the difference between spectral accuracies and divergent error bounds. In this paper we propose asymptotic analysis as a method for locating the optimal Gegenbauer reconstruction parameters. Such parameters are useful to applications of this reconstruction method that either seek to bound the number of Gegenbauer expansion coefficients or to control compression ratios. We then illustrate the effectiveness of our approach with the results from some numerical experiments.

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Section: Behavior Of Error Bounds For the Gegenbauer Methods In Applicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%