A study on multivariate interpolation by increasingly flat kernel functions

作者：Lee Yeon Ju; Micchelli Charles A; Yoon Jungho^*

来源：Journal of Mathematical Analysis and Applications, 2015, 427(1): 74-87.

DOI：10.1016/j.jmaa.2015.02.006

• Collocation matrix
• Wronskian
• Multivariate kernel interpolation
• Cauchy-Binet formula
• Radial basis function
• l'Hospital's rule

In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.

• 出版日期2015-7-1