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arXiv · 1710.05192

Kernel-based Approximation Methods for Generalized Interpolations: A Deterministic or Stochastic Problem?

Qi Ye
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Abstract

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.

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Qi Ye. 2017-10-14. Kernel-based Approximation Methods for Generalized Interpolations: A Deterministic or Stochastic Problem?. https://arxiv.org/abs/1710.05192

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