论文标题
贪婪地搜索最佳近似解决方案
Greedy search of optimal approximate solutions
论文作者
论文摘要
在本文中，我们制定了一个程序来处理一个依赖参数依赖的问题家族，而该问题通常不存在确切的解决方案。原始问题通过考虑相应的近似近似解决方案而放松，其最佳解决方案是很好的，其中最佳性是由最小规范要求确定的。该程序基于贪婪的算法，至少渐近地保留了kolmogorov近似率。为了提供算法的A-Priori估计值，应用Tychonff型正则化，从而为模型增加了一个附加参数。该理论是在一个抽象的理论框架中开发的，该框架允许其应用于各种问题。我们提出一个特定的示例，该例子考虑了一个不适的椭圆问题。在这种情况下，所需的一般假设转化为自然的均匀下限和上限，对所考虑的运算符的系数。
In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones, whose optimal solutions are well dfined, where the optimality is determined by the minimal norm requirement. The procedure is based upon greedy algorithms that preserve, at least asymptotically, Kolmogorov approximation rates. In order to provide a-priori estimates for the algorithm, a Tychonff-type regularization is applied, which adds an additional parameter to the model. The theory is developed in an abstract theoretical framework that allows its application to different kinds of problems. We present a specific example that considers a family of ill-posed elliptic problems. The required general assumptions in this case translate to rather natural uniform lower and upper bounds on coefficients of the considered operators.
