## View abstract

### Session III.5 - Information-Based Complexity

Monday, June 19, 17:00 ~ 17:30

## On Least Squares Approximation Based on Random or Optimal Data

### Mario Ullrich

#### JKU Linz, Österreich   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakaba7d8ea369ac339a7d716f4556bb553').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyaba7d8ea369ac339a7d716f4556bb553 = 'm&#97;r&#105;&#111;.&#117;llr&#105;ch' + '&#64;'; addyaba7d8ea369ac339a7d716f4556bb553 = addyaba7d8ea369ac339a7d716f4556bb553 + 'jk&#117;' + '&#46;' + '&#97;t'; var addy_textaba7d8ea369ac339a7d716f4556bb553 = 'm&#97;r&#105;&#111;.&#117;llr&#105;ch' + '&#64;' + 'jk&#117;' + '&#46;' + '&#97;t';document.getElementById('cloakaba7d8ea369ac339a7d716f4556bb553').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyaba7d8ea369ac339a7d716f4556bb553 + '\'>'+addy_textaba7d8ea369ac339a7d716f4556bb553+'<\/a>';

We study the $L_p$-approximation, $2\le p\le\infty$ of functions with the help of (unregularized) least squares methods based on "random" information, like function evaluations, and we want to compare this with the power of arbitrary algorithms based on arbitrary linear information, i.e., the best we can do theoretically.

Here, we survey on results of the past 5 years that eventually lead to a sharp comparison which showed that function evaluations are often enough for optimal results (in a worst-case sense).

Joint work with Matthieu Dolbeault (Sorbonne University, France), David Krieg (JKU Linz, Austria), Kateryna Pozharska (TU Chemnitz) and Tino Ullrich (TU Chemnitz).