## On asymptotically optimal methods of approximation by linear interpolating splines

- Nov. 22, 2005
- 2:30 p.m.
- LeConte 312

## Abstract

In this talk we shall present exact asymptotics of the optimal error in $L _ p$-norm, $1\leq p \leq \infty$, of linear spline interpolation of an arbitrary function $f \in C^2([0,1]^2)$.

We shall present review of existing results as well as a series of new ones. Proofs of these results lead to algorithms for construction of asymptotically optimal sequences of triangulations for linear interpolation. Similar results are obtained for near interpolation by bilinear splines.