A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Function Values Are Enough for $$L_2$$-Approximation

2020
*
Foundations of Computational Mathematics
*

AbstractWe study the $$L_2$$ L 2 -approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number $$e_n$$ e n is the minimal worst-case error that can be achieved with n function values, whereas the approximation number $$a_n$$ a n is the minimal worst-case error that can be achieved with n pieces of arbitrary linear information (like derivatives or Fourier coefficients). We show that $$\begin{aligned} e_n \,\lesssim \,

doi:10.1007/s10208-020-09481-w
fatcat:mwxrvsxbpbh6rkiua4a4tfwruq