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%% Benefits of Using Grid-Based Interpolation % Copyright 2015 The MathWorks, Inc. %% Section 1 % To illustrate the power of binary searches, consider the following % example. Before the advent of electronic credit card authorizations, the % only protection merchants had against fraudulent credit card purchases % was to compare the account number on each customer's credit card % against a list of "bad" account numbers. These lists were % bound booklets with tens of thousands of card numbers arranged in % ascending order. How many comparisons would be required to search through % a list of 10,000 account numbers for one sale? It turns out that for any % list of |n| ordered items, the maximum number of comparisons will be no % more than the number of times you can divide the list in half, or % |log2(n)|. Therefore, the credit card search will take no more than % |log2(10e3)| or about 13 comparisons. That's a pretty impressive % if you consider how many comparisons it would take to perform a % sequential search. %% % By contrast, consider a problem with a scattered data set. x = rand(20,1); y = rand(20,1); scatter(x,y) %% % To find the points in close proximity to a query point would require many % more operations. If your data can be approximated as a grid, grid-based % interpolation will provide substantial savings in computation and memory % usage.