Adaptive Quadrature

Numerical Analysis · Axiom Academy

Smart subdivision where it matters most 1. The Problem with Uniform Subdivision Composite rules use equal-width subintervals everywhere. But functions often have regions that are: Smooth — where few points suffice Rapidly varying — where many points are needed Estimate the error on each subinterval. If error is too large, subdivide that interval . If error is acceptable, stop and accept . Compare Simpson on [a,b] with Simpson on [a,m] + [m,b]: If they agree closely, accept. If not, the interval needs more work. Efficient for functions with localized difficulty No need to guess number of subintervals Overhead from recursion and error checking May struggle with singularities Need to set appropriate tolerance

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