quadrature_gauss

quadrature_gauss, demonstrates how the integral of a function f(x) can be estimated using Gauss quadrature.

The notes:

• quadrature_gauss.pdf
• quadrature_gauss.tex

Scripts and functions:

• cosfrac.m, a sample integrand, y = 1/(2+cos(x)).
• cosfrac_composite.m, uses an m-subinterval n-point composite Gauss rule to estimate the integral of 1/(2+cos(x)) from 0 to 2pi.
• cosfrac_int.m, returns the integral of cosfrac over the interval [0,2pi].
• expo.m, a test integrand, y = e^(-x^2).
• expo_gauss.m, uses an n-point Gauss rule to estimate the integral of e^(-x^2) from 0 to b.
• expo_int.m, returns the definite integral of e^(-x^2) over [a,b].
• gauss.m, returns points and weights for an n-point Gauss quadrature rule defined on the interval [-1,+1].
• gauss_ab.m, returns points and weights for an n-point Gauss quadrature rule defined on the interval [a,b].
• gauss_properties.m, verifies some properties of xi and rho in a Gauss rule.
• hump.m, evaluates the hump() function.
• hump_gauss.m, hump_gauss(tol) estimates the integral of hump() to within an estimated error of tol.
• hump_int.m, returns the value of the definite integral of hump() from a to b.
• newton.m, returns points and weights for an n-point Newton quadrature rule defined on the interval [-1,+1].
• newton_ab.m, returns points and weights for an n-point Newton quadrature rule defined on the interval [a,b].
• poly.m, a sample integrand, the function y = 10*x.^4 - 12*x.^3 + 2*x;
• poly_gauss.m, uses Gauss quadrature to estimate the integral of poly(x) over [-1,3].
• poly_int.m, returns the integral of y = 10*x.^4 - 12*x.^3 + 2*x over [a,b];
• quartic.m, evaluates the quartic() function.
• quartic_gauss.m, estimates the integral of the quartic() function over [a,b].
• quartic_gauss_m1p1.m, estimates the integral of the quartic() function over [-1,+1].
• quartic_int.m, returns the value of the definite integral of quartic() from a to b.

Images:

• gauss_quote.png