The Experts below are selected from a list of 2751 Experts worldwide ranked by ideXlab platform
Aditya Kumar Raghuvanshi - One of the best experts on this subject based on the ideXlab platform.
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On the Gibbs Phenomenon for
2020Co-Authors: Aditya Kumar RaghuvanshiAbstract:In this paper we have proved a theorem on the Gibbs Phenomenon for jN, pn, qnj- summability method which gives some new results and generalizes some previous known results.
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on the Gibbs Phenomenon for n p_n q_n summability method
Communications in Mathematics and Applications, 2014Co-Authors: Aditya Kumar RaghuvanshiAbstract:In this paper we have proved a theorem on the Gibbs Phenomenon for \(|N,p_n,q_n|\)-summability method which gives some new results and generalizes some previous known results.
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On The Gibbs Phenomenon for \(|N,p_n,q_n|\)-Summability Method
Communications in Mathematics and Applications, 2014Co-Authors: Aditya Kumar RaghuvanshiAbstract:In this paper we have proved a theorem on the Gibbs Phenomenon for \(|N,p_n,q_n|\)-summability method which gives some new results and generalizes some previous known results.
Gilbert G Walter - One of the best experts on this subject based on the ideXlab platform.
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Gibbs Phenomenon in higher dimensions
Journal of Approximation Theory, 2007Co-Authors: Hongtae Shim, Hans Volkmer, Gilbert G WalterAbstract:Gibbs' Phenomenon occurs for most orthogonal wavelet expansions in one dimension. It also exists in higher dimensions but fundamental concepts must be redefined. This is done for both separable and non-separable wavelet expansions in severable variables.
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hybrid sampling series associated with orthogonal wavelets and Gibbs Phenomenon
Journal of Applied Mathematics and Computing, 2003Co-Authors: Hongtae Shim, Gilbert G WalterAbstract:When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs Phenomenon.
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a general approach to Gibbs Phenomenon
Complex Variables, 2002Co-Authors: Gilbert G WalterAbstract:Gibbs Phenomenon occurs for most approximations based on standard orthogonal expansions, as well as for those based on integral operators. It also occurs in interpolations and other types of approximations. We consider a general approach to approximation based on delta sequences in an attempt to better understand the concept.
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Gibbs Phenomenon for sampling series and what to do about it
Journal of Fourier Analysis and Applications, 1998Co-Authors: Gilbert G Walter, Hongtae ShimAbstract:Gibbs' Phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' Phenomenon for orthogonal series do not for the associated sampling series.
Hongtae Shim - One of the best experts on this subject based on the ideXlab platform.
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Gibbs Phenomenon in higher dimensions
Journal of Approximation Theory, 2007Co-Authors: Hongtae Shim, Hans Volkmer, Gilbert G WalterAbstract:Gibbs' Phenomenon occurs for most orthogonal wavelet expansions in one dimension. It also exists in higher dimensions but fundamental concepts must be redefined. This is done for both separable and non-separable wavelet expansions in severable variables.
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hybrid sampling series associated with orthogonal wavelets and Gibbs Phenomenon
Journal of Applied Mathematics and Computing, 2003Co-Authors: Hongtae Shim, Gilbert G WalterAbstract:When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs Phenomenon.
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Gibbs Phenomenon for sampling series and what to do about it
Journal of Fourier Analysis and Applications, 1998Co-Authors: Gilbert G Walter, Hongtae ShimAbstract:Gibbs' Phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' Phenomenon for orthogonal series do not for the associated sampling series.
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on the Gibbs Phenomenon for wavelet expansions
Journal of Approximation Theory, 1996Co-Authors: Hongtae Shim, Hans VolkmerAbstract:It is shown that a Gibbs Phenomenon occurs in the wavelet expansion of a function with a jump discontinuity at 0 for a wide class of wavelets. Additional results are provided on the asymptotic behavior of the Gibbs splines and on methods to remove the Gibbs Phenomenon.
Shengtai Li - One of the best experts on this subject based on the ideXlab platform.
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application of gegenbauer polynomial expansions to mitigate Gibbs Phenomenon in fourier bessel series solutions of a dynamic sphere problem
International Journal for Numerical Methods in Biomedical Engineering, 2009Co-Authors: James R Kamm, Todd O Williams, Jerry S Brock, Shengtai LiAbstract:We utilize the inverse polynomial reconstruction (IPR) method to mitigate the Gibbs Phenomenon observed in Fourier–Bessel (FB) series. Gibbs Phenomenon is the oscillatory behavior that occurs near discontinuities when evaluating series solutions for Sturm–Liouville eigenvalue problems. We employ an approach that uses expansions of the solution in terms of Gegenbauer polynomials on each side of solution discontinuities, the location of which must be known in advance. The IPR solutions provide pointwise values that are more accurate than the truncated series solution, which are polluted by Gibbs Phenomenon. We apply this method to discontinuous solutions of a time dependent, linear elastic spherical shell problem, for which a series solution is derived in terms of a FB expansion. For the loading conditions and material properties, we consider the Gibbs Phenomenon in the FB solution for a perfectly elastic shell renders the numerically evaluated results unusable as an ‘exact’ solution for code verification analysis. We quantify the degree to which the IPR method eliminates the Gibbs Phenomenon in the computed solution. Copyright © 2009 John Wiley & Sons, Ltd.
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Application of Gegenbauer polynomial expansions to mitigate Gibbs Phenomenon in Fourier–Bessel series solutions of a dynamic sphere problem
International Journal for Numerical Methods in Biomedical Engineering, 2009Co-Authors: James R Kamm, Todd O Williams, Jerry S Brock, Shengtai LiAbstract:We utilize the inverse polynomial reconstruction (IPR) method to mitigate the Gibbs Phenomenon observed in Fourier–Bessel (FB) series. Gibbs Phenomenon is the oscillatory behavior that occurs near discontinuities when evaluating series solutions for Sturm–Liouville eigenvalue problems. We employ an approach that uses expansions of the solution in terms of Gegenbauer polynomials on each side of solution discontinuities, the location of which must be known in advance. The IPR solutions provide pointwise values that are more accurate than the truncated series solution, which are polluted by Gibbs Phenomenon. We apply this method to discontinuous solutions of a time dependent, linear elastic spherical shell problem, for which a series solution is derived in terms of a FB expansion. For the loading conditions and material properties, we consider the Gibbs Phenomenon in the FB solution for a perfectly elastic shell renders the numerically evaluated results unusable as an ‘exact’ solution for code verification analysis. We quantify the degree to which the IPR method eliminates the Gibbs Phenomenon in the computed solution. Copyright © 2009 John Wiley & Sons, Ltd.
John P Boyd - One of the best experts on this subject based on the ideXlab platform.
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trouble with gegenbauer reconstruction for defeating Gibbs Phenomenon runge Phenomenon in the diagonal limit of gegenbauer polynomial approximations
Journal of Computational Physics, 2005Co-Authors: John P BoydAbstract:To defeat Gibbs' Phenomenon in Fourier and Chebyshev series, Gottlieb et al. [D. Gottlieb, C.-W. Shu, A. Solomonoff, H. Vandeven, On the Gibbs Phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function, J. Comput. Appl. Math. 43 (1992) 81-98] developed a ''Gegenbauer reconstruction''. The partial sums of the Fourier or other spectral series are reexpanded as a series of Gegenbauer polynomials C"n^m(x), recovering spectral accuracy even in the presence of shock waves or other discontinuities. To achieve a rate of convergence which is exponential in N, however, Gegenbauer reconstruction, requires increasing the order m of the polynomials linearly with the truncation N of the series: m=@bN for some constant @b>0. When the order m is fixed, it is well-known that the Gegenbauer series converges as N->~ everywhere on x@?[-1,1] if f(x), the function being expanded, is analytic on the interval. But what happens in the diagonal limit in which m, N tend to infinity simultaneously? We show that singularities of f(x) off the real axis can destroy convergence of this diagonal approximation process in the sense that the error diverges for subintervals of x@?[-1,1]. Gegenbauer reconstruction must therefore be constrained to use a sufficiently small ratio of order m to truncation N. This ''off-axis singularity'' constraint is likely to impair the effectiveness of the reconstruction in some applications.