Abstract

The problem of finding a point of a linear manifold with a minimal weighted Chebyshev norm is considered. In particular, to such a problem, the Chebyshev approximation is reduced. An algorithm that always produces a unique solution to this problem is presented. The algorithm consists in finding relatively internal points of optimal solutions of a finite sequence of linear programming problems. It is proved that the solution generated by this algorithm is the limit to which the Hölder projections of the origin of coordinates onto a linear manifold converge with infinitely increasing power index of the Hölder norms using the same weight coefficients as the Chebyshev norm.

中文翻译：

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霍尔德投影到切比雪夫投影的收敛

摘要

考虑了寻找具有最小加权切比雪夫范数的线性流形的点的问题。特别地，对于这样的问题，切比雪夫近似被减小。提出了始终为该问题提供独特解决方案的算法。该算法在于找到线性规划问题的有限序列的最优解的相对内部点。证明了该算法产生的解是极限的极限，即坐标的原点在线性流形上的Hölder投影收敛到Hölder范数的幂指数无限增大，并且使用与Chebyshev范数相同的权重系数。