ORTHOGONAL POLYNOMIALS AND REGRESSION-BASED SYMMETRIC DERIVATIVES

Nathanial Burch; Paul E. Fishback

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ORTHOGONAL POLYNOMIALS AND REGRESSION-BASED SYMMETRIC DERIVATIVES

机译：正交多项式和基于回归的对称导数

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摘要

We demonstrate how certain types of symmetric derivatives originate from a simple least-squares regression problem involving discrete Cheby-shev polynomials. As the number of data points used in this regression tends to infinity, the resulting integrals, which involve Legendre polynomials, lead to Lanczos derivatives, a result that demonstrates how this latter entity is merely a continuous version of the symmetric derivative.

机译：我们演示了某些类型的对称导数如何源自涉及离散Cheby-shev多项式的简单最小二乘回归问题。由于此回归中使用的数据点数量趋于无穷大，因此涉及Legendre多项式的所得积分导致Lanczos导数，这一结果证明了后者的实体仅仅是对称导数的连续形式。

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来源
《Real analysis exchange》 |2007年第2期|p.597-608|共12页
作者
Nathanial Burch; Paul E. Fishback;
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作者单位

Department of Mathematics, Colorado State University, Fort Collins, CO, USA;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
symmetric and lanczos derivatives; regression; discrete chebyshev and legendre polynomials;

机译：对称和兰科斯导数;回归;离散契比雪夫和勒让德多项式;

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ORTHOGONAL POLYNOMIALS AND REGRESSION-BASED SYMMETRIC DERIVATIVES

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