关于双极函数的一致近似的注释

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/S1461157013000387

I. Moale, V. Pillwein

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引用次数: 1

摘要

我们考虑用多项式求1/(x-a)^2的最佳一致逼近的经典问题，其中在区间$[-\!1美元1]。首先，利用符号计算工具推导出低次最佳逼近多项式的显式表达式，然后用椭圆函数给出该问题的参数解。然后，基于解满足的pell型方程，再次利用符号计算推导出最佳一致逼近多项式系数的递推关系。

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A note on uniform approximation of functions having a double pole

We consider the classical problem of finding the best uniform approximation by polynomials of $1/(x-a)^2,$ where $a>1$ is given, on the interval $[-\! 1,1]$ . First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.