I am a little bit confused about the difference between the H-Adaptive Integration and adaptive quadrature algorithms, AFAIK:
- Both break down the entire region of integration into smaller sub-regions.
- Both apply a quadrature rule: Each sub-region is tackled using a pre-defined numerical integration rule (like Midpoint, Trapezoidal, etc.).
- Both adaptively refine the error in a sub-region if it is too large.
After all, is there any difference in both techniques?