球面上的非线性逼近

Our goal in this project is to study nonlinear approximation for the classes of multivariate smooth functions on the unit sphere S^d, on the ball B^d and on the simplex T^d. We concern ourself with the best m-term approximation problems. The asymptotic estimates of m-term approximation and corresponding optimal algorithm would be given. The research would push the development of approximation theory in the relative fields, and it also has applications in numerical analysis, computational complexity, nonlinear functional analysis, statistical estimation, image and signal processing.

本项目研究球面S^d、球体B^d 和单形T^d 等紧集上的多元光滑函数类的非线性逼近问题，主要考虑最佳m-项逼近的特征，给出m-项逼近渐近阶的估计，以及找出实现此逼近阶的渐近最优算法。预期所得结果不但对多元函数逼近理论的相关方向带来推动，而且对数值分析, 计算复杂性，非线性泛函分析，统计估计，图像信号处理等应用学科也有借鉴作用。