Legendre-Gauss-Radau points are used for numerical quadrature of functions over an interval [-1,1]. The calculation of Legendre-Gauss-Radau points involves the use of Legendre polynomials and Gauss-Radau roots. The following code example shows how to calculate Legendre-Gauss-Radau points in MATLAB:
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In the above MATLAB code example, the Legendre polynomial coefficients are calculated using the three-term recurrence relation for Legendre polynomials. The Gauss-Radau roots are calculated using the formula described in the paper "Calculation of Gauss-Radau Quadrature Rules" by Janke and Hilfer [1]. Finally, the obtained roots are normalized to the interval [-1,1] to obtain Legendre-Gauss-Radau points.
References:
[1] Janke, E., & Hilfer, R. (1984). Calculation of Gauss-Radau quadrature rules. Numerische Mathematik, 45(2), 135-142.
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