标题： 个体函数的稀疏逼近 显示英文标题

标题： Sparse approximation of individual functions

摘要： 在个体函数的逼近特性渐近行为的两种不同设置下的结果被呈现。 首先，我们讨论稀疏逼近中的一个经典问题。 对于给定函数类中的任何个体函数，其相对于给定字典的最佳稀疏逼近误差序列是否比该函数类上的相应上界衰减得更快？ 其次，我们讨论贪心类型算法的稀疏逼近。 我们证明，对于给定类中的任何个体函数，如果我们利用算法之前迭代中的一些信息，就可以改进贪心算法逼近误差收敛速率的上界。 我们将这类界限称为后验界限。 显示英文摘要

摘要： Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual function from a given function class its sequence of errors of best sparse approximations with respect to a given dictionary decays faster than the corresponding supremum over the function class? Second, we discuss sparse approximation by greedy type algorithms. We show that for any individual function from a given class we can improve the upper bound on the rate of convergence of the error of approximation by a greedy algorithm if we use some information from the previous iterations of the algorithm. We call bounds of this type a posteriori bounds.