i am applying Regula Falsi method in C++ but the problem is with == operator when F(x3) become 0 then if (fabs( f(x3))==0 should stop and comes out from the loop but it does not stop why why why.... like output below after 12th iteration f(x3)=0 but if(fabs(f(x3)==0)) does not run. loop does not stop it should not go to 13th iteration
float f(float x)
{
float f_x;
f_x= pow(x,3)+(3*x)-5;
return f_x;
}
int main(int argc, char** argv)
{
float a,b,tol,x3;
int itr,n;
cout << "enter the iterations";
cin >> itr;
cout << "enter the interval a";
cin >> a;
cout <<"enter the interval b";
cin >> b;
cout << "enter the toleration";
cin >> tol;
cout.setf(std::ios_base::fixed, std::ios_base::floatfield);
cout.precision(5);
//cout<<"fa="<<f(a)<<"fb"<<f(b);
cout<<"n\t\ta\t\tb\t\tx3\t\tf(a)\t\tf(b)\t\tf(x3)" <<endl;
if (f(a)*f(b)<0 && a<b)
{
for (n=0;n<itr;n++)
{
x3=a-((b-a)*f(a))/(f(b)-f(a));
cout << "xx"<<fabs(f(x3));
if (fabs( f(x3))==0)
{
cout << "Solution"<<fabs(f(x3));
break;
}
else
{
cout<<n+1 <<"\t\t"<<a <<"\t\t"<<b <<"\t\t"<<x3<<"\t\t"<<f(a)
<<"\t"<<f(b)<<"\t\t"<<f(x3) <<endl;
if(f(x3)*f(a)<0)
b=x3;
else
if(f(x3)*f(b)<0)
a=x3;
}
}
}
else
cout<< "No Solution Exist";
return 0;
}
OUTPUT
enter the iterations13
enter the interval a1
enter the interval b2
enter the toleration1
**n a b x3 f(a) f(b) f(x3)**
1 1.00000 2.00000 1.10000 -1.00000 9.00000 -0.36900
2 1.10000 2.00000 1.13545 -0.36900 9.00000 -0.12980
3 1.13545 2.00000 1.14774 -0.12980 9.00000 -0.04487
4 1.14774 2.00000 1.15197 -0.04487 9.00000 -0.01542
5 1.15197 2.00000 1.15342 -0.01542 9.00000 -0.00529
6 1.15342 2.00000 1.15391 -0.00529 9.00000 -0.00181
7 1.15391 2.00000 1.15408 -0.00181 9.00000 -0.00062
8 1.15408 2.00000 1.15414 -0.00062 9.00000 -0.00021
9 1.15414 2.00000 1.15416 -0.00021 9.00000 -0.00007
10 1.15416 2.00000 1.15417 -0.00007 9.00000 -0.00003
11 1.15417 2.00000 1.15417 -0.00003 9.00000 -0.00001
12 1.15417 2.00000 1.15417 -0.00001 9.00000 0.00000
13 1.15417 2.00000 1.15417 -0.00000 9.00000 0.00000
The issue here is not floating-point precision; it's the tolerance that you're willing to accept in your result. In most cases, regula falsi will get you closer and closer to the correct result as you run through more iterations, but it will not give you the exact answer. So the decision you have to make is, how close do you want the result to be? That's a tradeoff between the real-world requirements for accuracy and the time it takes to get the result; more accuracy requires more computing time. So choose a tolerance that's acceptable for your task, and repeat the loop until the result is within that tolerance. If it turns out to be too slow, you'll have to increase the tolerance.