Numerical methods. Note 3


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Lectures

Adaptive algorithms with error estimates. (!)
Gaussian quadratures and orthogonal polynomials.
Gauss-Kronrod formulas.
QUADPACK library.

Problems

Make a detailed algorithm for an adaptive integration routine along the following lines:

	estimate the integral and error over the given interval
	if error is less than the accuracy goal
		then return the integral and error
		else divide the interval in two and recurse

Implement adaptive integration routines with 3-point close and 4-point open formulas.
Consider the accuracy parameter of your integrator. Implement both the absolute accuracy and relative accuracy parameters in your integrator. (One can use recursive functions in C and Fortran90 -- here is an example).
Compare your integrator with one of the QAG* routines from the QUADPACK library. The fortran version, qag.f, is here while the c version "gsl_integration_qag" is included in GNU/GSL (here is an example).