论文标题
通过在不确定性定量中应用的定期内核晶格点插值快速近似
Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification
论文作者
论文摘要
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng, Kritzer, Hickernell (Constr. Approx., 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver.本文的主要贡献是对近似问题的应用，用于对椭圆形偏微分方程的不确定性定量，在随机变量中，随机字段给定的扩散系数，在Kaarnioja，Kuo，Kuo，Kuo，Sloan，Sloan，Sloan。本文提供了完整的错误分析，并提供了确保良好（但不可避免地不是最佳）收敛速率和误差限制的晶格的完整详细信息。数值实验支持该理论。
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng, Kritzer, Hickernell (Constr. Approx., 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver. The main contribution of the paper is the application to the approximation problem for uncertainty quantification of elliptic partial differential equations, with the diffusion coefficient given by a random field that is periodic in the stochastic variables, in the model proposed recently by Kaarnioja, Kuo, Sloan (SIAM J. Numer. Anal., 2020). The paper gives a full error analysis, and full details of the construction of lattices needed to ensure a good (but inevitably not optimal) rate of convergence and an error bound independent of dimension. Numerical experiments support the theory.
