Topics in nonlinear approximation

近些年来，逼近理论和数值分析中的非线性方法受到了广泛的关注。这主要是因为非线性数值方法的表现比线性数值方法好得多，而且非线性流形对函数的逼近阶比线性空间元素的逼近阶好得多。作者将继续研究各种非线性逼近流形的逼近空间(包括单变量和多变量环境)。特别是，将研究和修改新的自适应算法，以产生更令人满意的数值结果。此外，作者还将继续在约束非线性逼近的各个领域进行研究，进一步发展这一领域，在曲线插补与逼近、计算机辅助几何设计(CAGD)、计算机辅助制造(CAM)等方面有着广泛的应用。

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.