Differential Equations Solutions 98

Differential Equations Solutions 98 - Method 2 Method 3...

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108 Chapter 18. Solutions: Case Study: Multidimensional Integration 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Pseudorandom samples 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 First two quasirandom coordinates 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Second two quasirandom coordinates 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Third two quasirandom coordinates Figure 18.1. 500 pseudo-random points (upper left). 500 quasi-random points: coordinates 1-2 (upper right), coordinates 3-4 (lower left), coordinates 5-6 (lower right). CHALLENGE 18.5. The following table gives the absolute value of the errors in the estimates from each of the four methods. n Method 1
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Unformatted text preview: Method 2 Method 3 Method 4 10 3.65e-03 1.11e-02 4.67e-03 1.50e-02 100 1.35e-03 3.38e-03 1.02e-03 2.49e-03 1000 2.85e-03 2.38e-04 1.22e-05 3.00e-04 10000 1.57e-03 1.14e-03 1.75e-04 4.10e-05 100000 4.97e-04 1.72e-04 1.44e-05 5.14e-06 Convergence rates can be determined from the slope of a straight line Ft to the logs of each set of errors. The best results were obtained by Method 4, using quasi-random numbers in Method 2. Method 3, importance sampling, was also quite good. CHALLENGE 18.6. No answer provided....
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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