I have a function evaluated on a regular 5D grid with 21 points per dimension (so $21^{5}$ points total).I need to evaluate the integral of the function over all 5 dimensions, so I was planning on using one of the composite Newton-Cotes formulae (i.e. trapezium rule, Simpson's rule, Boole's rule etc.)I'm wondering:Assuming we can't re-evaluate the function on a different grid, is there a way of approaching this that is significantly better than Newton-Cotes?If we are using Newton-Cotes, is higher-order always better? More specifically is it always better to divide the data into a smaller number of intervals evaluated with a higher-order scheme rather than a larger number of intervals evaluated with a lower-order scheme?Thanks!
Choice of Newton-Cotes formulae for regularly gridded multi-dimensional data
numerical analysis;quadrature;integration