How should I determine the number of quadrature points when using Gaussian quadrature integration?

Question

For integration of polynomials, the number of qradrature points can be determined easily according to the $(2N-1)$ rule. While in most cases, it's not necessary to use Gaussian quadrature for simple polynomials since they can be calculated analytically, what we encounter in reality are generally complex integrands, such as rational functions.

In this case, how can we determin an appropriate number of quadrature points so that we can get a somewhat acceptible solution, and at the same time will not lead to a waste of computational efforts?

acceptable solution is the problem. Could you define it ? – Claude Leibovici Nov 14 '15 at 08:10 — Claude Leibovici, Nov 14 '15 at 08:10

score 1 · Accepted Answer · answered Nov 14 '15 at 08:15

1

May be, the idea would be to use Gauss–Kronrod rules which will double the number of quadratic points without compting the function values of a lower-order estimate. Stop the process when you think that the solution is acceptable for you.

answered Nov 14 '15 at 08:15

Claude Leibovici

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How should I determine the number of quadrature points when using Gaussian quadrature integration?

1 Answers1