2017/10/14 by Ye, Qi
#41A65 #46E22 #65D05 #65R99 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1710.05192
In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a covariance kernel which is defined on the dual space of the Banach space. The kernel-based probability measure provides a numerical tool to construct and analyze the kernel-based estimators conditioned on non-noise data or noisy data including algorithms and error analysis. Same as meshfree methods, we can also obtain the kernel-based approximate solutions of elliptic partial differential equations by the kernel-based probability measure.