BEST APPROXIMATION AND INTEGRAL INTERPOLATION IN THE SPACES OF CONTINUOUS FUNCTIONS

连续函数空间中的最佳逼近和积分插值

• 批准号: 11640190
• 负责人: KITAHARA Kazuaki
• 金额: $ 0.83万
• 依托单位: KWANSEI GAKUIN UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640190/
• 关键词: best approximation; interpolation; Chebyshev polynomials; チュビシェフ多項式; チェビシェフ系; ルメのアルゴリズム

(1) Best approximation by integral Chebyshev systems.To consider an algorithm obtaining best approximations, we have investigated and proved results on best approximations by integral Chebyshev systems.(2) Integral interpolation and Chebyshev polynomials.By numerical experiments, we have formed important conjectures on minimum of the norms of the Lagrange interpolation operators and a chracterization of Chebyshev polynomials in the second kind.(3) An algorithm obtaining best approximations.We have ontained an algorithm best approxmations by integral Chebyshev systems like the Remez second algorithm.(4) Approximation by polynomials.We have extended a theorem of Jackson type to K dimensions.

(1)积分Chebyshev系统的最佳逼近为了考虑获得最佳逼近的算法，我们研究并证明了积分Chebyshev系统的最佳逼近的结果。(2)积分插值与Chebyshev多项式，通过数值实验，我们得到了关于拉格朗日插值算子范数极小值的重要结果，并给出了第二类Chebyshev多项式的一个刻划。(3)一种获得最佳逼近的算法。我们得到了积分Chebyshev系统的一个最佳逼近算法，如Remez第二算法。(4)用多项式逼近.我们把杰克逊型定理推广到K维.

项目成果

Kazuaki Kitahara and Ken-ichi Kuri: "On a Theorem of Jackson Type in K Dimensions"Numerical Functional Analysis and Optimization. 21. 465-470 (2000)

Kazuaki Kitahara 和 Ken-ichi Kuri：“关于 K 维 Jackson 型定理”数值泛函分析和优化。

Kazuaki Kitahara: "Some Problems on Polynomial Approximation"Unsolved Problems on Mathematics for the 21 Century. (印刷中).

Kazuaki Kitahara：“多项式逼近的一些问题”《21 世纪数学未解决的问题》（出版中）。

Kazuaki Kitahara, Toshinao Okada and Yasuhiro Sakamori: "Some Problems on Polynomial Approximation"Unsolved Problems on Mathematics for the 21st Century (Eds. J.M.Abe and S.Tanaka).. to appear.

Kazuaki Kitahara、Toshinao Okada 和 Yasuhiro Sakamori：“多项式逼近的一些问题”未解决的 21 世纪数学问题（J.M.Abe 和 S.Tanaka 编辑）.. 出现。