題  目：On regularized barycentric interpolation formulae（論正則化重心插值公式）

内容簡介：Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. Regularized barycentric interpolation formulae are efficient interpolation method to realize noise reduction, which involve $/ell_2$ and $/ell_1$ regularization terms, respectively. Under some spectral conditions, regularized barycentric interpolation formulae can be computed in O(N) operations. In this talk, we introduce modified regularized Lagrange interpolation formula based on the so-called first barycentric interpolation, given by C. Jacobi in 1825. Then we focus on the numerical stability of these regularized interpolation formulae in terms of backward and forward stability. We also involve the stability with respect to extrapolation, illustrating regularized modified Lagrange interpolation is better than regularized barycentric interpolation in extrapolation. Moreover, we employ Chebyshev points (1st and 2nd kind, respectively) and Legendre points as interpolation nodes to test numerical stability.

報告人：西南财經大學  安聰沛  副教授

報告人簡介：博士生導師。主要從事點集分布理論以及計算方法應用研究，在球面t-設計，高震蕩函數積分計算、插值理論和方法有較好的研究結果。主持國家自然科學基金二項，省部級自然基金一項，中央高校基金二項，在SIAM J. Numer.Anal.,J.Comput.and Appl. Math.,Appl.Math and Comput.等計算數學期刊發表論文多篇。多次應邀訪問香港理工大學，香港中文大學，香港大學，香港城市大學，中國科學院數學與系統科學研究院等著名學術機構。

時  間：2019年7月1日（周一）下午4：00始

地  點：南海樓330室

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