Decomposing a Function for Numerical Integration

[ecastro]

Is their a tutorial or a reference on how to decompose a function, specifically Fourier and Legendre decomposition, for numerical integration? The method I am going to use for the numerical integration is the Gauss Quadrature, and I suppose I need to decompose my function for the rule to work.

Thank you in advance.

 

[drvrm]

Is their a tutorial or a reference on how to decompose a function, specifically Fourier and Legendre decomposition, for numerical integration? The method I am going to use for the numerical integration is the Gauss Quadrature, and I suppose I need to decompose my function for the rule to work.

to decompose a function in gauss quadrature method ...one does a trial and error approach leading to a stable value.
however it depends on the nature of the function which is being integrated...
a common/general approach is to fit more number of quadrature points in those regions where function is varying in a complex manner and keep less points in 'smooth varying regions like asymptotic regions where the function is falling off linearly.