A study of numerical integration based on Legendre polynomial and RLS algorithm. (English) Zbl 1386.65080
Summary: 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.
MSC:
| 65D10 | Numerical smoothing, curve fitting |
| 65D30 | Numerical integration |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 93E24 | Least squares and related methods for stochastic control systems |
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