The most compact algorithm for Simpson's rule??
12-16-2015, 12:57 AM (This post was last modified: 12-16-2015 01:53 PM by Namir.)
Post: #15
 Namir Senior Member Posts: 743 Joined: Dec 2013
RE: The most compact algorithm for Simpson's rule??
Here is a version that iterates one less time to calculate the integral:

Code:
Given function f(x), integration interval [A, B] and N divisions, where N is even. To calculate the integral of f(x) for X=A to x=B using Simpson's Rule h=(B-A)/N Sum=f(A)+f(B) C=4 Do   A=A+h   Sum = Sum + C*f(A)   C=6-C   N=N-1 Loop Until N=1 Area=h/3*Sum

The last iteration multiplies f(A) by 4 and leaves C with the value of 2. The initial value of Sum is initialized as f(A)+f(B). By controlling the loop with a counter, we can have a compact version that does not not do extra calculations.

Namir
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 Messages In This Thread The most compact algorithm for Simpson's rule?? - Namir - 12-12-2015, 04:24 PM RE: The most compact algorithm for Simpson's rule?? - Thomas Klemm - 12-12-2015, 05:44 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-12-2015, 08:29 PM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-12-2015, 09:16 PM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-12-2015, 09:44 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-12-2015, 08:28 PM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-12-2015, 09:05 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-12-2015, 10:54 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-12-2015, 11:02 PM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-14-2015, 09:04 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-15-2015, 12:09 AM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-15-2015, 07:12 AM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-13-2015, 01:52 AM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-13-2015, 01:27 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-16-2015 12:57 AM RE: The most compact algorithm for Simpson's rule?? - Dieter - 12-16-2015, 01:25 PM RE: The most compact algorithm for Simpson's rule?? - Namir - 12-16-2015, 01:54 PM

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