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

  • * Corresponding author: Wen Tan

    * Corresponding author: Wen Tan 

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

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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  • 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.

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


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  • Table 1.  The calculation results

    examplesThis proposed methodrer of Hybrid[20]
    Example 10.321970599192823.7271e-179.6947e-13
    Example 226.083287714147141.4155e-163.7148e-14
    Example 30.341962491330271.8001e-113.7947e-8
     | Show Table
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