Uniform approximation of sgn x by polynomials and entire functions
Uniform approximation of sgn x by polynomials and entire functions
复制标题
通过多项式和整个函数对 sgn x 进行均匀逼近
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Yuditskii
中科院分区：
文献类型：
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作者：
A. Eremenko;P. Yuditskii
在1877年，E。I. Zolotarev [19，2]发现，从元素函数方面，明确的表达在两个间隔的结合下，给定程度m-的合理函数M-在两个间隔[-1中都非常接近sgn（x）[-1 ，-a]∪[a，1]。在这个论文。为了比较，我们在这里提到| x |的均匀统一的结果。
In 1877, E. I. Zolotarev [19, 2] found an explicit expression, in terms ofelliptic functions, of the rational function of given degree mwhich is uni-formly closest to sgn(x) on the union of two intervals [−1,−a] ∪[a,1]. Thisresult was subject to many generalizations, and it has applications in electricengineering.Surprisingly, to the best of our knowledge, the similar problem for poly-nomials was not solved yet, so we investigate it in this paper.For comparison, we mention here the results on the uniform approxima-tion of |x|