Basic HTML version of Foils prepared 22 February 98

Foil 3 Sequential Romberg Integration

From Parallel Computation Illustrated with Adaptive Integration CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Nancy J McCracken
1 Recall that when you repeatedly apply Simpson's rule, halving the interval each time, you can use old values of the function. Furthermore, there is a convenient pattern to the Simpson coefficients.
2 In our program, we start with an initial set of Xi's for which we calculate f values and save them in an array oldf. Then for each iteration of Simpson's rule, we collect the new values in an array newf. The result uses 2 * oldf and 4*newf (with exceptions for the endpoints).
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