Interpolation with uncoupled separable matrix-valued kernels

Abstract

In this paper we consider the problem of approximating vector-valued functions over a domain Ω. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial functions and which can be viewed as an extension of the scalar-valued case. These spaces seem promising, when modelling correlations between the target function components, as the components are not learned independently of each other. We focus on the interpolation with such matrix-valued kernels. We derive error bounds for the interpolation error in terms of a generalized power-function and we introduce a subclass of matrix-valued kernels whose power-functions can be traced back to the power-function of scalar-valued reproducing kernels. Finally, we apply these kind of kernels to some artificial data to illustrate the benefit of interpolation with matrix-valued kernels in comparison to a componentwise approach. 

Haasdonk B., Santin G., Wittwar D. (2018) "Interpolation with uncoupled separable matrix-valued kernels " Dolomites Research Notes on Approximation, 11(3), 23-39. DOI: 10.14658/PUPJ-DRNA-2018-3-4  
Year of Publication
2018
Journal
Dolomites Research Notes on Approximation
Volume
11
Issue Number
3
Start Page
23
Last Page
39
Date Published
11/2018
ISSN Number
2035-6803
Serial Article Number
4
DOI
10.14658/PUPJ-DRNA-2018-3-4
Issue
Section
SpecialIssue3