Gauss Integration

Orthogonal Polynomials obey recurrence relation

Tuesday 6 September 2011

Gauss Quadrature

Gauss-Legendre

w(x) = 1

approximate g(x)

i is the ith root of Pi(x)

Exact when g(x) polynomialof order < 2n -1

Tuesday 6 September 2011

For our purposes we only need the table with

w(x) and x.The weights are

symmetric in + and -

Error is

Tuesday 6 September 2011

Gauss-Laguerre Gauss-Hermite

Tuesday 6 September 2011

Tuesday 6 September 2011

Note the singularity at x = 1

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011

Tuesday 6 September 2011