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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Fast approximation on the real line

## Fast approximation on the real lineAdd to your list(s) Download to your calendar using vCal - Arieh Iserles (University of Cambridge)
- Wednesday 07 August 2019, 14:00-15:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact INI IT. GCS - Geometry, compatibility and structure preservation in computational differential equations Abstract: While approximation theory in an interval is thoroughly understood, the real line represents something of a mystery. In this talk we review the state of the art in this area, commencing from the familiar Hermite functions and moving to recent results characterising all orthonormal sets on $L_2(-\infty,\infty)$ that have a skew-symmetric (or skew-Hermitian) tridiagonal differentiation matrix and such that their first $n$ expansion coefficients can be calculated in $O(n \log n)$ operations. In particular, we describe the generalised Malmquist–Takenaka system. The talk concludes with a (too!) long list of open problems and challenges. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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