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9f135d5 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 | // Secant method for root finding
// Iterative method using finite differences (no derivatives needed)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define TOL 1e-10
#define MAX_ITER 50
#define NUM_TRIALS 15000
// Test functions
double f1(double x) {
return x * x * x - x - 2.0; // Root near 1.52
}
double f2(double x) {
return exp(x) - 3.0 * x; // Root near 0.619
}
double f3(double x) {
return sin(x) - 0.5 * x; // Root near 1.896
}
double secant(double (*f)(double), double x0, double x1, double tol, int max_iter) {
for (int i = 0; i < max_iter; i++) {
double f0 = f(x0);
double f1_val = f(x1);
if (fabs(f1_val) < tol) {
return x1;
}
if (fabs(f1_val - f0) < 1e-15) {
return NAN; // Division by zero
}
double x2 = x1 - f1_val * (x1 - x0) / (f1_val - f0);
if (fabs(x2 - x1) < tol) {
return x2;
}
x0 = x1;
x1 = x2;
}
return x1;
}
int main() {
clock_t start = clock();
double sum = 0.0;
int found = 0;
for (int iter = 0; iter < NUM_TRIALS; iter++) {
double root;
if (iter % 3 == 0) {
root = secant(f1, 1.0, 2.0, TOL, MAX_ITER);
} else if (iter % 3 == 1) {
root = secant(f2, 0.0, 1.0, TOL, MAX_ITER);
} else {
root = secant(f3, 1.0, 2.0, TOL, MAX_ITER);
}
if (!isnan(root)) {
sum += root;
found++;
}
}
clock_t end = clock();
double time_spent = (double)(end - start) / CLOCKS_PER_SEC;
printf("Secant method: %d trials, %.6f seconds\n",
NUM_TRIALS, time_spent);
printf("Found %d roots, average: %.10f\n", found, sum / found);
return 0;
}
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