题目：On regularized barycentric interpolation formulae（论正则化重心插值公式）

内容简介：Barycentric interpolation is arguably the method of choice for numericalpolynomial 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.

报告人：西南财经大学安聪沛副教授

报告人简介：博士生导师。主要从事点集分布理论以及计算方法应用研究，在球面t-设计，高震荡函数积分计算、插值理论和方法有较好的研究结果。主持国家自然科学基金二项，省部级自然基金一项，中央高校基金二项，在SIAM J. Numer.Anal.,J.Comput.and Appl. Math.,Appl.Math and Comput.等计算数学期刊发表论文多篇。多次应邀访问香港理工大学，香港中文大学，香港大学，香港城市大学，中国科学院数学与系统科学研究院等著名学术机构。

时间：2019年7月1日（周一）下午4：00始

地点：南海楼330室

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信息科学技术学院

2019年6月26日