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Gibbs Phenomenon V: Recovering Exponential Accuracy from Collocation Point Valuesof a Piecewise Analytic Function

机译：Gibbs现象V：从分段解析函数的搭配点值恢复指数精度

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The paper presents a method to recover exponential accuracy at all points(including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or an highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct an uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods. Gibbs phenomenon, Collocation, Fourier, Chebyshev, Legendre, Gegenbauer, Exponential accuracy.

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作者
Gottlieb, D.; Shu, C. W.;
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年度 1994
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总页数 19
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Interpolation; Approximation(Mathematics); Analytic functions; Accuracy; Discontinuities; Intervals; Polynomials; Points(Mathematics); Legendre functions; Chebyshev functions; Fourier analysis;

机译：插值;逼近（数学）;解析函数;精度;不连续性;区间;多项式;点（数学）; Legendre函数; Chebyshev函数;傅里叶分析;

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专利

1. ON THE GIBBS PHENOMENON .3. RECOVERING EXPONENTIAL ACCURACY IN A SUB-INTERVAL FROM A SPECTRAL PARTIAL SUM OF A PIECEWISE ANALYTIC FUNCTION [J] . Gottlieb D., Shu CW. SIAM Journal on Numerical Analysis . 1996,第1期

机译：关于吉布斯现象.3。从分段解析函数的频谱局部和中的一个子区间恢复指数精度
2. ON THE GIBBS PHENOMENON .4. RECOVERING EXPONENTIAL ACCURACY IN A SUBINTERVAL FROM A GEGENBAUER PARTIAL SUM OF A PIECEWISE ANALYTIC FUNCTION [J] . Gottlieb D., Shu CW. Mathematics of computation . 1995,第211期

机译：关于吉布斯现象.4。从分段分析函数的Gengenbauer偏和的子区间中恢复指数精度
3. Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities [J] . Zheng Chen, Chi-Wang Shu Journal of Computational and Applied Mathematics . 2014,第Null期

机译：从具有端点奇点的光滑函数的并置点值恢复指数精度
4. A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon [C] . John, P. Boyd International conference on spectral and high order methods . 2011

机译：基于欧拉总和加速的证据，恢复指数（几何）收敛率的傅立叶级数与Gibbs现象的函数
5. ANALYTICAL DETERMINATION OF THE PRESENT WORTH DISTRIBUTION FUNCTION OF PROJECTS WITH EXPONENTIALLY DECLINING CASH FLOWS. [D] . LIMA, HUMBERTO. 1975

机译：现金流量呈指数下降的项目的当前价值分布函数的解析确定。
6. Modeling the covariates effects on the hazard function by piecewise exponential artificial neural networks: an application to a controlled clinical trial on renal carcinoma [O] . Marco Fornili, Patrizia Boracchi, Federico Ambrogi, 2018

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7. On the Gibbs phenomenon IV: Recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function [O] . David Gottlieb, Chi-wang Shu 1995

机译：关于吉布斯现象IV：从分段分析函数的Gegenbauer局部和恢复子区间的指数精度

Gibbs Phenomenon V: Recovering Exponential Accuracy from Collocation Point Valuesof a Piecewise Analytic Function

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