Correction to: Kernel-based interpolation at approximate Fekete points
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Correction to: Kernel-based interpolation at approximate Fekete points Toni Karvonen1,2
¨ a¨ 1 · Ken’ichiro Tanaka3 · Simo Sarkk
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Correction to: Numerical Algorithms https://doi.org/10.1007/s11075-020-00973-y •
An equation in Section 2.1 has been corrected to n |f (xx ) − sf (xx )| = f, K(·, x ) − K(·, x k )uk (xx ) k=1 HK () n ≤ f HK () K(·, x ) − K(·, x k )uk (xx ) k=1
=: f HK () PXn (xx )
HK ()
The online version of the original article can be found at https://doi.org/10.1007/s11075-020-00973-y. Toni Karvonen
[email protected] Simo S¨arkk¨a [email protected] Ken’ichiro Tanaka [email protected] 1
Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland
2
The Alan Turing Institute, London, UK
3
Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan
Numerical Algorithms
from
n K(·, x k )uk (xx ) |f (xx ) − sf (xx )| = f K(·, x ) − k=1 HK () n ≤ f HK () K(·, x ) − K(·, x k )uk (xx ) k=1
=: f HK () PXn (xx ). • •
HK ()
An ∞ inline equation in Section ∞ 2.2 has been corrected to f f, ϕ ϕ from f = HK () =1 =1 ϕ HK () ϕ . An equation in Section 2.2 has been corrected to f, K(·, x )HK () = =
∞
=
ϕ , ϕk HK () f, ϕ HK () ϕk (xx )
,k=1 ∞
f, ϕ HK () ϕ (xx )
=1
= f (xx ) from K(·, x )HK () = =
∞
ϕ ϕk HK () ϕ HK () ϕk (xx )
,k=1 ∞
ϕ HK () ϕ (xx )
=1
= f (xx ). • •
An inline equation in Section 3.2 has been corrected to f = f, ϕ HK () from f = ϕ HK () . An equation in Section 3.3 has been corrected to ∞ f, ψ 2 L2 (μ) 2 2 HK () = f ∈ L (μ) : f HK () =
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