/*
 *  newton.c :  Newton-Verfahren für
 *
 *              f(x) := cos(x)-x = 0
 *
 *  x0 .......  Startwert
 *  xacc .....  Genauigkeit der Näherungslösung
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define   MAXITER   20


/*
 *  f(x)
 */
double f( double x ) {
    return( cos(x) - x );
}


/*
 *  df(x)/dx
 */
double df( double x ) {
    return( -sin(x) - 1.0 );
}


int main( void ) {

    double x0, xacc, x, xn, dx;
    int    j;

    printf("x0 : ");
    scanf("%lf", &x0);
    printf("xacc : ");
    scanf("%lf", &xacc);

    x = x0;

    /*  Iterationsschleife  */

    for (j = 1; j <= MAXITER; j++) {

        dx = f(x) / df(x);
        xn = x - dx;

        printf("x = %14.7e   |xn - x| = %14.7e\n", x, fabs(dx));

        if (fabs(dx) < xacc) {
           printf("s = %14.7e\n", x);
           break;
        }

        x = xn;
    }

    if (j > MAXITER) {
       printf("newton: MAXITER ueberschritten\n");
       exit(1);
    }

    return(0);
}