Scholarlink

Abstract <p>On a standard simplex in <i>n</i>-dimensional Euclidean space, we introduce a function <i>H</i>(<i>x</i>) whose value at a point <i>x</i> = (<i>x</i><sub>1</sub>, …, <i>x</i><sub><i>n</i></sub>) is equal to the harmonic mean of the numbers <i>x</i><sub>1</sub>, …, <i>x</i><sub><i>n</i></sub>. The problem of the best uniform approximation of the function <i>H</i>(<i>x</i>) on the simplex by linear functions is considered. A unique solution to the problem is given. It has complete alternance. The existence of complete alternance guarantees the strong uniqueness of the solution. An exact constant of strong uniqueness is found.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Example of Complete Alternance in the Multidimensional Case

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • V. N. Malozemov,
  • A. V. Plotkin

摘要

Abstract

On a standard simplex in n-dimensional Euclidean space, we introduce a function H(x) whose value at a point x = (x1, …, xn) is equal to the harmonic mean of the numbers x1, …, xn. The problem of the best uniform approximation of the function H(x) on the simplex by linear functions is considered. A unique solution to the problem is given. It has complete alternance. The existence of complete alternance guarantees the strong uniqueness of the solution. An exact constant of strong uniqueness is found.