Errors in Random vs. Methodical Sampling

• Comparison of errors

  • methodical approach
  • Monte Carlo integration

• MC error vanishes much more slowly for increasing n

• For one-dimensional integrals, MC offers no advantage

• This conclusion changes as the dimension d of the integral increases

  • methodical approach
  • MC integration

• MC “wins” at about d = 4

independent of dimension!

for example (Simpson’s rule)

d = 236 points, 361/2 = 6 in each row

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