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Namir · (This post was last modified: 07-29-2015 11:39 AM by Namir.)

(07-24-2015 04:35 PM)Gilles Wrote:
(07-24-2015 12:01 PM)tigger Wrote: I would like to program the Bisection Methode.
Is there anybody who can help me with it.
Hi

It seems there is a problem with your example as there is no root for this function between 1 and 2

here is an example (not optimised), in RPL, aprox mode with a modified function (X^5-5) :

Code:

'F(X)=X^5-5' DEFINE 1. 2. « IF OVER F OVER F > THEN SWAP END 0. -> A B C « DO A B + 2. / DUP 'C' STO IF 'F(C)<0' THEN 'A' STO ELSE 'B' STO END UNTIL 'ABS(F(C))<0.01' END C » »

Your code assumes F(A)<0 and that's risky, because if F(A)>0 your implementation will not work. The traditional Bisection algorithm uses the test F(A)*F(C)>0 instead to determine if we set A=C (when that condition is true) and B=C otherwise.

I assume the RPL code should be:

Code:

'F(X)=X^5-5' DEFINE

 1. 2.

« 

 IF OVER F OVER F > THEN SWAP END

 0. -> A B C

 « 

  DO

   A B + 2. / DUP 'C' STO  

   IF 'F(A)*F(C)>0' THEN 'A' STO ELSE 'B' STO END

  UNTIL 'ABS(F(C))<0.01' END

  C

 »

»

Namir