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CAdvanced Functions ❯ Finding Equation Roots
<06.10>
// Finding a Function Root Using the Bisection Method // Finds roots of the equations // g(x) = 0 and h(x) = 0 // on a specified interval [x_left, x_right] using the bisection method. #include <stdio.h> #include <math.h> #define FALSE 0 #define TRUE 1 #define NO_ROOT -99999.0 // equation #1 double g(double x) { return (5 * pow(x, 3.0) - 2 * pow(x, 2.0) + 3); } // equation #2 double h(double x) { return (pow(x, 4.0) - 3 * pow(x, 2.0) - 8); } // Implements the bisection method for finding a root of a function f. // Returns a root if signs of fp(x_left) and fp(x_right) are different. // Otherwise returns NO_ROOT. double bisect(double x_left, /* input - endpoints of interval in */ double x_right, /* which to look for a root */ double epsilon, /* input - error tolerance */ double f(double farg)) /* input - the function */ { double x_mid, /* midpoint of interval */ f_left, /* f(x_left) */ f_mid, /* f(x_mid) */ f_right; /* f(x_right) */ int root_found; /* flag to indicate whether root is found */ /* Computes function values at initial endpoints of interval */ f_left = f(x_left); f_right = f(x_right); /* If no change of sign occurs on the interval there is not a unique root. Exit function and return NO_ROOT */ if (f_left * f_right > 0) { /* same sign */ printf("\nMay be no root in [%.7lf, %.7lf]", x_left, x_right); return (NO_ROOT); } /* Searches as long as interval size is large enough and no root has been found */ root_found = FALSE; /* no root found yet */ while (fabs(x_right - x_left) > epsilon && !root_found) { /* Computes midpoint and function value at midpoint */ x_mid = (x_left + x_right) / 2.0; f_mid = f(x_mid); if (f_mid == 0.0) { /* Here's the root */ root_found = TRUE; } else if (f_left * f_mid < 0.0) {/* Root in [x_left,x_mid]*/ x_right = x_mid; } else { /* Root in [x_mid,x_right]*/ x_left = x_mid; } /* Trace loop execution - print root location or new interval */ if (root_found) printf("\nRoot found at x = %.7lf, midpoint of [%.7lf, %.7lf]", x_mid, x_left, x_right); else printf("\nNew interval is [%.7lf, %.7lf]", x_left, x_right); } /* If there is a root, it is the midpoint of [x_left, x_right] */ return ((x_left + x_right) / 2.0); } int main(void) { double x_left, x_right, /* left, right endpoints of interval */ epsilon, /* error tolerance */ root; /* Get endpoints and error tolerance from user */ printf("Enter interval endpoints > "); scanf("%lf%lf", &x_left, &x_right); printf("Enter tolerance > "); scanf("%lf", &epsilon); /* Use bisect function to look for roots of g and h */ printf("\n\nFunction g"); root = bisect(x_left, x_right, epsilon, g); if (root != NO_ROOT) printf("\n g(%.7f) = %e\n", root, g(root)); printf("\n\nFunction h"); root = bisect(x_left, x_right, epsilon, h); if (root != NO_ROOT) printf("\n h(%.7f) = %e\n", root, h(root)); return (0); }
Hergestellt in Deutschland / Made in Germany
Enter interval endpoints > -1.0 1.0 Enter tolerance > 0.001 Function g New interval is [-1.0000000, 0.0000000] New interval is [-1.0000000, -0.5000000] New interval is [-0.7500000, -0.5000000] New interval is [-0.7500000, -0.6250000] New interval is [-0.7500000, -0.6875000] New interval is [-0.7500000, -0.7187500] New interval is [-0.7343750, -0.7187500] New interval is [-0.7343750, -0.7265625] New interval is [-0.7304688, -0.7265625] New interval is [-0.7304688, -0.7285156] New interval is [-0.7294922, -0.7285156] g(-0.7290039) = -2.697494e-05 Function h May be no root in [-1.0000000, 1.0000000]
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