Iterations.java

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package ostap.chyselni;

/**
 *
 * @author Ostap.Andrusiv
 */
public class Iterations {

    /**
     * @param args
     */
    private static double epsilon;
    public static String output;
    public static int n;

    public Iterations() {
        prepare();
    }

    /**
     * Function who's 0 we are to find
     *
     * @param x
     * @return result of f(x)
     */
    private static double f(double x) {
        // f(x) = x-sin(x)-0.25;
        return x - Math.sin(x) - 0.25d;
    }

    /**
     * derivative of f(x)
     *
     * @param x
     * @return calculates derivative of f() in x
     */
    private static double fD(double x) {
        // f(x) = x-sin(x)-0.25;
        // f'(x) = 1-cos(x);
        return 1 - Math.cos(x);
    }

    private static void prepare() {
        epsilon = 0.00001d;
        output = "";
        n=0;
    }
    /**
     * Secant Method implementation
     *
     * @param x
     *            , x1 are boundaries of the secant
     * @param epsilon
     *            approximation
     * @return root of equation f(x)=0;
     */
    public static double secantMethod(double x, double x1) {
        prepare();

        while (Math.abs(x1 - x) > epsilon) {
            x = x1 - (x1 - x) * f(x1) / (f(x1) - f(x));
            x1 = x - (x - x1) * f(x) / (f(x) - f(x1));
            output += x1 + "\n";
            ++n;
        }

        return x1;
    }

    /**
     * finds root by Newton's Method
     *
     * @param x
     *            starting argument
     * @param epsilon
     *            approximation
     * @return root
     */
    public static double NewtonsMethod(double x) {
        prepare();

        double x1 = x - f(x) / fD(x);
        while (Math.abs(x - x1) > epsilon) {
            x = x1;
            x1 = x - f(x) / fD(x);
            output += x1 + "\n";
            ++n;
        }

        return x1;
    }

    /**
     * equivalent f(x)=0 : x=psi(x);
     *
     * @param x
     *            argument
     * @return x for next iteration;
     */
    private static double phi(double x) {
        // that's because we have f(x)=x-sin(x)-0.25;
        return Math.sin(x) + 0.25;
    }

    /**
     * finds root by Simple Iteration Method
     *
     * @param x
     *            starting argument
     * @param epsilon
     *            approximation
     * @return root
     */
    public static double SimpleIterationMethod(double x) {
        // f(x) = x-sin(x)-0.25
        // f(x) == 0
        // f(x) + x == x
        // phi(x) == x=-sin(x)-0.25
        //phi' = |-cos(x)|<1
        prepare();

        double x1 = phi(x);
        while (Math.abs(x1 - x) > epsilon) {
            x = x1;
            x1 = phi(x);
            output += x1 + "\n";
            ++n;
        }

        return x1;
    }
}