Unformatted text preview: the dimension d is large so that methods like quad would be forced to use a lot of function evaluations. CHALLENGE 18.2. See challenge2.m on the website. CHALLENGE 18.3. A sample program is available on the website. Importance sampling produces better estimates at lower cost: see the answer to Challenge 4 for detailed results. CHALLENGE 18.4. The results are shown in Figure 18.1. The pseudorandom points from MATLAB’s rand are designed to have good statistical properties, but they leave large gaps in space. The quasirandom points are both more predictable and more evenly distributed. They tend to lie on diagonal lines, with longer strings as the coordinate number increases. Other algorithms for generating quasirandom points avoid this defect. 107...
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 Fall '11
 Dr.Robin
 Numerical Analysis, Derivative, Monte Carlo method, QuasiMonte Carlo method, digit accuracy

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