Differential Equations Solutions 95

Differential Equations Solutions 95 - 105 3500 KRS Explicit...

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105 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 2500 3000 3500 k C(k) KRS Explicit count Figure 17.9. Counts obtained by the KRS algorithm and by explicit count- ing for a 4 × 4 lattice. For KRS we set the probabilities to 0 . 5 , the number of steps between records to ± =4 , and the total number of steps to 10 5 . Because ± was so small, the samples were highly correlated, but the estimates are still quite good. C (0) C (1) C (2) C (3) C (4) C (5) C (6) C (7) C (8) 2 × 2 142 2 × 3 17 1 1 3 3 × 3 11 24 4 5 6 1 8 4 × 4 1 24 224 1044 2593 3388 2150 552 36 6 × 6 1 60 1622 26172 281514 2135356 11785382 48145820 146702793 (b) One of the more interesting programming issues in this problem is the data structure . If we keep track of each edge of the lattice, then we need to enumerate rules for deciding whether two edges can be covered at the same time. For example,
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