Porovnání Newtonovy a Gaussovy numerické integrace

Abstract

Numerical integration methods are based on replacing the integral with its polynomial interpolation. For smooth functions, the efficiency of the method depends only on the choice of interpolation, ie the quadrature nodes, with the number which we call the quadrature order. We will look not only at the Lagrange interpolation polynomial, but also on the system of orthogonal polynomials, especially on the Legendrous polynomials. Once we compile the Newton-Cotes and Gauss-Legendre quadrature. So we compare them in terms of convergence and stability.