Data commit

Task/Steffensens-method/C/steffensens-method.c

@@ -0,0 +1,69 @@
+#include <stdio.h>
+#include <math.h>
+
+double aitken(double (*f)(double), double p0) {
+    double p1 = f(p0);
+    double p2 = f(p1);
+    double p1m0 = p1 - p0;
+    return p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0);
+}
+
+double steffensenAitken(double (*f)(double), double pinit, double tol, int maxiter) {
+    double p0 = pinit;
+    double p = aitken(f, p0);
+    int iter = 1;
+    while (fabs(p - p0) > tol && iter < maxiter) {
+        p0 = p;
+        p = aitken(f, p0);
+        ++iter;
+    }
+    if (fabs(p - p0) > tol) return nan("");
+    return p;
+}
+
+double deCasteljau(double c0, double c1, double c2, double t) {
+    double s = 1.0 - t;
+    double c01 = s * c0 + t * c1;
+    double c12 = s * c1 + t * c2;
+    return s * c01 + t * c12;
+}
+
+double xConvexLeftParabola(double t) {
+    return deCasteljau(2.0, -8.0, 2.0, t);
+}
+
+double yConvexRightParabola(double t) {
+    return deCasteljau(1.0, 2.0, 3.0, t);
+}
+
+double implicitEquation(double x, double y) {
+    return 5.0 * x * x + y - 5.0;
+}
+
+double f(double t) {
+    double x = xConvexLeftParabola(t);
+    double y = yConvexRightParabola(t);
+    return implicitEquation(x, y) + t;
+}
+
+int main() {
+    double t0 = 0.0, t, x, y;
+    int i;
+    for (i = 0; i < 11; ++i) {
+        printf("t0 = %0.1f : ", t0);
+        t = steffensenAitken(f, t0, 0.00000001, 1000);
+        if (isnan(t)) {
+            printf("no answer\n");
+        } else {
+            x = xConvexLeftParabola(t);
+            y = yConvexRightParabola(t);
+            if (fabs(implicitEquation(x, y)) <= 0.000001) {
+                printf("intersection at (%f, %f)\n", x, y);
+            } else {
+                printf("spurious solution\n");
+            }
+        }
+        t0 += 0.1;
+    }
+    return 0;
+}