Topics in nonlinear approximation

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Nonlinear methods in Approximation Theory and Numerical Analysis received much attention in recent years. This is mostly due to the fact that nonlinear numerical methods perform much better than linear ones, and that the order of approximation of functions from nonlinear manifolds is much better than the order of approximation by the elements of linear spaces. The proposer will continue his investigation of approximation spaces for various nonlinear approximation manifolds (both in univariate and multivariate settings). In particular, new adaptive algorithms will be investigated and modified to yield numerically more satisfactory results. Also, the proposer will continue his research in various areas of constrained nonlinear approximation further developing this field having numerous applications in curve interpolation and approximation, computer-aided geometric design (CAGD), computer-aided manufacturing (CAM), etc.