### Wednesday, July 12

## IP7

Nonlinear Approximation

2:00 PM-2:45 PM

*Room: Rio Mar 5 *

*Chair: Tony F. Chan, University of California, Los Angeles, USA *

Nonlinear approximation is the theoretical underpinning of large portions of image/signal processing and numerical PDEs. For example, most wavelet based compression and noise removal algorithms are based on *n*-term approximation. Adaptive algorithms in PDEs can often be viewed as a form of nonlinear spline approximation. This talk will highlight the current understanding of nonlinear approximation, especially those aspects that are most important in applications. The speaker will discuss free partition spline approximation, adaptive methods, *n*-term approximation, and greedy algorithms. He will also look to the future and outline some of the pressing problems in this field.

**Ronald A. DeVore**

*Department of Mathematics*

*University of South Carolina, Columbia, USA*