Multidimensional Integration

Numerical Analysis · Axiom Academy

LESSON Multidimensional Integration 1. Double Integrals: Iterated Quadrature For a double integral, apply 1D quadrature rules iteratively: First integrate over y for each x, then integrate over x. 2. Product Rules and the Curse Using n points per dimension in d dimensions requires n^d total points! Random sampling offers a dimension-independent convergence rate: Error is O(1/√N) regardless of dimension ! Use low-discrepancy sequences (Halton, Sobol) instead of random points for better convergence: O(log(N)^d / N).

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