False Position Method - Example Code

Example Code

C code was written for clarity instead of efficiency. It was designed to solve the same problem as solved by the Newton's method and secant method code: to find the positive number x where cos(x) = x3. This problem is transformed into a root-finding problem of the form f(x) = cos(x) - x3 = 0.

#include #include double f(double x) { return cos(x) - x*x*x; } /* s,t: endpoints of an interval where we search e: half of upper bound for relative error m: maximal number of iterations */ double FalsiMethod(double s, double t, double e, int m) { int n,side=0; double r,fr,fs = f(s),ft = f(t); for (n = 1; n <= m; n++) { r = (fs*t - ft*s) / (fs - ft); if (fabs(t-s) < e*fabs(t+s)) break; fr = f(r); if (fr * ft > 0) { t = r; ft = fr; if (side==-1) fs /= 2; side = -1; } else if (fs * fr > 0) { s = r; fs = fr; if (side==+1) ft /= 2; side = +1; } else break; } return r; } int main(void) { printf("%0.15f\n", FalsiMethod(0, 1, 5E-15, 100)); return 0; }

After running this code, the final answer is approximately 0.865474033101614

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