Mathematics I / Vectorised Computation and Libraries
Practice question · True or false

Monte Carlo error falls like 1/N1/\sqrt{N} regardless of the dimension, which is why it wins in high dimensions.

Hints
  1. How does a grid method scale with dimension?
  2. A grid needs points exponential in the dimension.
Show the answer

True

Why

True. Grid-based quadrature needs kdk^{d} points in dd dimensions, hopeless past a handful, while Monte Carlo's 1/N1/\sqrt{N} rate is dimension-free. It is slow in one dimension and unbeatable in twenty, which is why it dominates in finance, physics and rendering.

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