Computation of Gaussian Quadrature Nodes and Corresponding Coefficients for Arbitrary Points

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Resource Overview

This program calculates Gaussian quadrature nodes and their corresponding weighting coefficients for arbitrary points, while also implementing the Lagrange interpolation formula for enhanced numerical integration accuracy.

Detailed Documentation

In this program, we not only compute Gaussian quadrature nodes and their corresponding weighting coefficients for arbitrary points, but also develop a comprehensive interpolation algorithm. The algorithm is based on the Lagrange interpolation formula, which provides improved accuracy when computing mathematical functions. By employing this approach with numerical implementation features such as node selection through root-finding algorithms and coefficient calculation via orthogonal polynomial properties, we can explore mathematical domains more extensively, thereby enhancing our mathematical proficiency and technical skills. The code includes functions for generating recurrence relations for orthogonal polynomials, solving for quadrature nodes using numerical methods like Newton-Raphson iteration, and computing weights through analytical integration of Lagrange basis functions.

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