论文标题
连续函数的最佳通用有理近似的算法
An algorithm for best generalised rational approximation of continuous functions
论文作者
论文摘要
本文的动机是开发一种优化方法，用于解决Chebyshev合理和广义理性近似问题中出现的优化问题，其中将近似值构造为线性形式的比率（基础函数的线性组合）。线性形式的系数受到优化，基本函数是连续函数。众所周知，在广义有理近似问题中的目标函数是准凸。在本文中，我们还证明了更强的结果，目的函数在Penot和Quang的意义上是伪convex。然后，我们开发数值方法，这些方法对于广泛的伪符号函数有效，并在广义理性近似问题上测试它们。
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios of linear forms (linear combinations of basis functions). The coefficients of the linear forms are subject to optimisation and the basis functions are continuous function. It is known that the objective functions in generalised rational approximation problems are quasi-convex. In this paper we also prove a stronger result, the objective functions are pseudo-convex in the sense of Penot and Quang. Then we develop numerical methods, that are efficient for a wide range of pseudo-convex functions and test them on generalised rational approximation problems.
