newton_raphson_root.c File Reference

Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm. More...

#include <complex.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

Include dependency graph for newton_raphson_root.c:

Macros
#define	ACCURACY   1e-10
	solution accuracy

Functions
double complex	func (double complex x)
	Return value of the function to find the root for.
double complex	d_func (double complex x)
	Return first order derivative of the function.
int	main (int argc, char **argv)
	main function

Detailed Description

Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm.

Author

Krishna Vedala

Function Documentation

d_func()

double complex d_func

(

double complex

x

)

Return first order derivative of the function.

\(f'(x)\)

{ return 2. * x; }

func()

double complex func

(

double complex

x

)

Return value of the function to find the root for.

\(f(x)\)

{
    return x * x - 3.; /* x^2 = 3 - solution is sqrt(3) */
    // return x * x - 2.; /* x^2 = 2 - solution is sqrt(2) */
}

main()

int main	(	int	argc,
		char **	argv
	)

main function

{
    double delta = 1;
    double complex cdelta = 1;
 
    /* initialize random seed: */
    srand(time(NULL));
 
    /* random initial approximation */
    double complex root = (rand() % 100 - 50) + (rand() % 100 - 50) * I;
 
    unsigned long counter = 0;
    /* iterate till a convergence is reached */
    while (delta > ACCURACY && counter < ULONG_MAX)
    {
        cdelta = func(root) / d_func(root);
        root += -cdelta;
        counter++;
        delta = fabs(cabs(cdelta));
 
#if defined(DEBUG) || !defined(NDEBUG)
        if (counter % 50 == 0)
        {
            double r = creal(root);
            double c = cimag(root);
 
            printf("Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n", counter,
                   r, c >= 0 ? '+' : '-', c >= 0 ? c : -c, delta);
        }
#endif
    }
 
    double r = creal(root);
    double c = fabs(cimag(root)) < ACCURACY ? 0 : cimag(root);
 
    printf("Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n", counter, r,
           c >= 0 ? '+' : '-', c >= 0 ? c : -c, delta);
 
    return 0;
}

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