A study of numerical integration based on Legendre polynomial and RLS algorithm

Hongguang Xiao; Wen Tan; Dehua Xiang; Lifu Chen; Ning Li

doi:10.3934/naco.2017028

Article Contents

2017, Volume 7, Issue 4: 457-464. Doi: 10.3934/naco.2017028

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A study of numerical integration based on Legendre polynomial and RLS algorithm

1.
Changsha University of Science and Technology, Changsha 410114, P. R. China
2.
Measurement and Testing Research Institute of Hunan Province, Changsha 410014, P. R. China

^* Corresponding author: Wen Tan
^* Corresponding author: Wen Tan

The reviewing process of the paper was handled by Nanjing Huang as Guest Editors

Received: March 2016

Revised: July 2017

Published online: October 2017

The first author is supported by The National Natural Science Foundation of China (41201468) and The National Nonprofit Industry Research (201510003-5).

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Abstract

A quadrature rule based on Legendre polynomial functions is proposed to find approximate values of definite integrals in this paper. This method uses recursive least squares (RLS) algorithm to compute coefficients of Legendre polynomial fitting functions, and then approximately computes values of definite integrals by using obtained the coefficients. The main advantage of this approach is its efficiency and simple applicability. Finally some examples are given to test the convergence and accuracy of the method.

Keywords:

Numerical integration; Legendre polynomial; curve fitting; RLS.

Mathematics Subject Classification: Primary: 65D10, 65D30; Secondary: 42C10, 93E24.

Citation:

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Table 1. The calculation results

examples	This proposed method		rer of Hybrid[20]
examples	1	rer	rer of Hybrid[20]
Example 1	0.32197059919282	3.7271e-17	9.6947e-13
Example 2	26.08328771414714	1.4155e-16	3.7148e-14
Example 3	0.34196249133027	1.8001e-11	3.7947e-8

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