Romberg Algorithm for Integration
Jay Pedersen
Explanation
This estimates the integral value over interval [a,b] of input function f(x).
Routine: romberg Parameters: f - function to be integrated a, b - interval of integration N - number of columns to generated (zero-based) print_table - true or false, true to display generated table
Algorithm
Examples
Restrictions
The input function must be Riemann integrable.
Notes
(1) Uses the trapezoid rule (with uniform spacing) to generate the first column. Uses properties of the error formula for the trapezoid rule integration (which is defined using the second derivative of the function). (2) To check if the method is working for a function; check table entries (set print_table = true); to see if the following holds:
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References
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