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Show ALL Forums  > Science/philosophy  > Method of False Position? No.      Home login  
 AUTHOR
 lateā„¢
Joined: 2/1/2010
Msg: 2
Method of False Position? No.Page 1 of 1    
It's "Regula", "Regla" is a municipality of Havana, Cuba.

http://en.wikipedia.org/wiki/False_position_method

In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method.
 abelian
Joined: 1/12/2008
Msg: 4
Method of False Position? No.
Posted: 6/24/2010 12:09:49 AM
I guess an numerical equation-solving method could be called a "root-finding method", if you call an equation's zeros "roots".

That's the definition of the root of an equation. For example, x = 2 is one zero of the equation:
x^2 - 4 = 0, since x^2 - 2 = (x + 2)(x -2), which is zero for x = +/-2.

Often Successive Substitutions (often called Successive Approximations) seems the easiest and most convenient method, especially when using an ordinary calculator with only one memory, even though it might not converge as fast as Newton's.

Iteration may not actually get the right answer even if you use the exact analytical expression when you use a calculator or a computer. The choice of numerical method depends on the type of equation you are trying to solve, machine precision, etc. Here's an example of an iterated solution using the exact recursion relation between Bessel functions (using double precision) starting with the correct values for J_0 and J_1 to get J_10, compared with the correct value from the c math library. The iterated version is not only wrong, it's not even the right sign:

Order Iterated Value Correct Value
2  +0.1149034848   +0.1149034849
3   +0.0195633535   +0.0195633540
4   +0.0024766362   +0.0024766390
5   +0.0002497361   +0.0002497577
6   +0.0000207248   +0.0000209383
7   -0.0000010385   +0.0000015023
8   -0.0000352638   +0.0000000942
9   -0.0005631822   +0.0000000052
10 -0.0101020166   +0.0000000003

I'm not sure how this is going to format here, but this generated the table:
--------------------------------------------

#include<stdio.h>
#include<math.h>

double jn(int m, double y);

int main(){

  double x,J[11];
  int n;

  J[0] = (double)0.7651976866;
  J[1] = (double)0.4400505857;

  fprintf(stdout, "\nOrder Iterated Value Correct Value\n\n");

  for(n=1; n<=9; n++){
   J[n+1] = 2.0*n*J[n] - J[n-1];
   fprintf(stdout, "%-2d %+1.10f %+1.10f\n", n+1, J[n+1], jn(n+1, (double)1.0));
 }

  fprintf(stdout, "\n");
  exit(0);
}
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Show ALL Forums  > Science/philosophy  > Method of False Position? No.