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 () =