69 lines
2.0 KiB
Java
69 lines
2.0 KiB
Java
import java.util.Optional;
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public class Steffensen {
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static double aitken(double p0) {
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double p1 = f(p0);
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double p2 = f(p1);
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double p1m0 = p1 - p0;
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return p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0);
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}
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static Optional<Double> steffensenAitken(double pinit, double tol, int maxiter) {
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double p0 = pinit;
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double p = aitken(p0);
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int iter = 1;
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while (Math.abs(p - p0) > tol && iter < maxiter) {
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p0 = p;
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p = aitken(p0);
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iter++;
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}
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if (Math.abs(p - p0) > tol) return Optional.empty();
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return Optional.of(p);
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}
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static double deCasteljau(double c0, double c1, double c2, double t) {
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double s = 1.0 - t;
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double c01 = s * c0 + t * c1;
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double c12 = s * c1 + t * c2;
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return s * c01 + t * c12;
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}
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static double xConvexLeftParabola(double t) {
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return deCasteljau(2.0, -8.0, 2.0, t);
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}
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static double yConvexRightParabola(double t) {
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return deCasteljau(1.0, 2.0, 3.0, t);
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}
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static double implicitEquation(double x, double y) {
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return 5.0 * x * x + y - 5.0;
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}
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static double f(double t) {
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double x = xConvexLeftParabola(t);
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double y = yConvexRightParabola(t);
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return implicitEquation(x, y) + t;
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}
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public static void main(String[] args) {
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double t0 = 0.0;
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for (int i = 0; i < 11; ++i) {
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System.out.printf("t0 = %3.1f : ", t0);
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Optional<Double> t = steffensenAitken(t0, 0.00000001, 1000);
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if (!t.isPresent()) {
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System.out.println("no answer");
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} else {
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double x = xConvexLeftParabola(t.get());
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double y = yConvexRightParabola(t.get());
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if (Math.abs(implicitEquation(x, y)) <= 0.000001) {
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System.out.printf("intersection at (%f, %f)\n", x, y);
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} else {
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System.out.println("spurious solution");
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}
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}
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t0 += 0.1;
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}
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}
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}
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