## Asymptotically Optimal Methods of Interpolation by Linear and Other Types of Splines

- April 11, 2006
- 3:30 p.m.
- LeConte 405

## Abstract

The exact asymptotics will be discussed in the talk, of the optimal error in the weighted L_p-norm, of linear spline interpolation of an arbitrary C^2([0,1]^2)-function. A review of earlier results, as well as a series of new ones, will be presented. The proofs of these results generated algorithms of construction of asymptotically optimal triangulation sequences for linear interpolation. Similar results are also obtained for near interpolation by linear and biquadratic splines. If time permits, analogous multivariate results will be also discussed.