Modifications of the first Remez algorithm
Modifications of the first Remez algorithm
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第一个 Remez 算法的修改
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
R. Reemtsen
中科院分区：
文献类型：
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作者：
R. Reemtsen
本文证明了解紧B子集mathbb{R}^s上线性和非线性Chebyshev逼近问题的第一Remez算法的几种修正的收敛性。虽然原始形式的第一个Remez算法需要在每次迭代中确定所有B上的误差函数的全局最大值，但这里给出的算法是基于它足以计算网格$B_{k + 1} $上的第k个误差函数的最大值，其中${ {B_k } }_{kgeqq 0} $是B中密度趋于零的有限点集的规定序列。不同的解释，切比雪夫近似问题，不使用全网格$B_k $在B，但只有他们的小子集的离散化的一些结果，提供。本文最后给出了一些求解线性多元问题的数值例子。
This paper proves the convergence of several modifications of the first Remez algorithm for the solution of linear and nonlinear Chebyshev approximation problems on compact $B subset mathbb{R}^s $. While the first Remez algorithm in its original form requires the determination of the global maximum of the error function on all of B in each iteration, the algorithms given here are based on its being sufficient to compute the maximum of the kth error function on a grid $B_{k + 1} $, where ${ {B_k } }_{k geqq 0} $ is a prescribed sequence of finite-point sets in B with density tending to zero. Interpreted differently, some results on the discretization of Chebyshev approximation problems, which do not use full grids $B_k $ in B but only small subsets of them, are provided. The paper concludes with some numerical examples for the solution of linear multivariate problems.