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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 pseudo-random points from MATLABs rand are designed to have good statistical properties, but they leave large gaps in space. The quasi-random 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 quasi-random points avoid this defect. 107...
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- Fall '11