Lab1 pop

newton 1================================================
#include <iostream>
#include <math.h>
#include<conio.h>
using namespace std;

float f(float x) {
	return x * exp(x) - 1;

}

float g(float x) {

	return exp(x)*(x + 1);
}


void main() {
	const float eps =1e-5;
	const int ITMAX = 100;
	float x = 0;
	int n = 0;



	while ((fabs(f(x)) > eps) && n<=ITMAX) {

		x = (x - f(x) / g(x));

		n = n + 1;

	}
	if (n > ITMAX)
		cout << "Numarul maxim de iteratii depasit";
	else {
		cout << "Valoarea aproximativa a solutiei este" << x << endl;
		cout << "Numarul de iteratii este:" << n;
	}

	_getch();

}

NEWTON 2===================================================================
#include <iostream>
#include <math.h>
#include<conio.h>
#include<stdio.h>


using namespace std;

void newton_radical(double x, int itmax, double eps, int p, double a) {
	int n = 1;
	while ((fabs(pow(x, p) - a) > eps) && (n <= itmax)) {
		x = (1.0 / p) * ((x * (p - 1)) + (a / (pow(x, p - 1))));
		n = n + 1;
	}
	if (n > itmax) {
		printf("In %d nu a fost realizata aproximarea dorita", itmax);
		printf("\n");
	}
	else {
		printf("Aproximarea obtinuta este %lf", x);
		printf("\n");
	}

}

void main() {
	double a;
	int p;
	double x;
	double eps;
	int itmax;
	printf("Introduceti Aproximatia initiala: ");
	scanf_s("%lf", &x);
	printf("\n");
	printf("Precizia de eroare: ");
	scanf_s("%lf", &eps);
	printf("\n");
	printf(" Introduceti numarul de iteratii maxime: ");
	scanf_s("%d", &itmax);
	printf("\n");
	printf("Introduceti numarul real: ");
	scanf_s("%lf", &a);
	printf("\n");
	printf(" Introduceti ordinul radicalului: ");
	scanf_s("%d", &p);
	printf("\n");
	newton_radical(x, itmax, eps, p, a);
	_getch();
}

NEWTON 3=============================================================================
#include <iostream>
#include <math.h>
#include<conio.h>
#include<stdio.h>


using namespace std;

double fun(double x) {
	return((x*exp(x)) - 1);
}


void secanta(double x0, double x1, int itmax, double eps) {
	int n = 2;
	double x;
	while ((fabs(fun(x1) > eps) && (n <= itmax))) {
		x = x1 - ((fun(x1) * (x1 - x0)) / (fun(x1) - fun(x0)));
		x0 = x1;
		x1 = x;
		n = n + 1;
	}
	if (n > itmax) {
		printf("In %d nu a fost realizata aproximarea dorita", itmax);
		printf("\n");
	}
	else {
		printf("Aproximarea obtinuta este %lf", x);
		printf("\n");
	}

}

void main() {
	double x0, x1;
	double eps;
	int itmax;
	printf("Aproximatia initiala x0= ");
	scanf_s("%lf", &x0);
	printf("\n");
	printf("Aproximatia initiala x1= ");
	scanf_s("%lf", &x1);
	printf("\n");
	printf("Diferenta de eroare: ");
	scanf_s("%lf", &eps);
	printf("\n");
	printf("Numarul de iteratii maxime: ");
	scanf_s("%d", &itmax);
	printf("\n");
	secanta(x0, x1, itmax, eps);
	_getch();
}

NEWTON 4=============================================
#include <iostream>
#include <math.h>
#include<conio.h>
#include<stdio.h>


using namespace std;

double fun(double x) {
	return exp(-x);
}


void aprox_succes(double x, int itmax, double eps) {
	int n = 1;
	while ((fabs(x - fun(x)) > eps) && (n <= itmax)) {
		x = fun(x);
		n = n + 1;
	}
	if (n > itmax) {
		printf("In %d nu a fost realizata aproximarea dorita", itmax);
		printf("\n");
	}
	else {
		printf("Aproximarea obtinuta este %lf", x);
		printf("\n");
		printf("Numarul de iteratii efectuate: %d", n);
	}

}
void main() {
	double x;
	double eps;
	int itmax;
	printf("Aproximatia initiala x= ");
	scanf_s("%lf", &x);
	printf("\n");
	printf("Diferenta de eroare: ");
	scanf_s("%lf", &eps);
	printf("\n");
	printf("Numarul de iteratii maxime: ");
	scanf_s("%d", &itmax);
	printf("\n");
	aprox_succes(x, itmax, eps);
	_getch();
}