METODOS NUMERICOS

MÉTODO DE DESCENSO RÁPIDO O GRADIENTE

package metodo_numerico_udo;

import java.util.Scanner;

public class Gradiente {

public void Descenso_Gradiente()

{

double r[] = {1,1};

double u[] = new double[2];

double tol = 0;

int k = 0;

Scanner s = new Scanner (System.in);

System.out.println ("Ingrese Tolerancia");

tol=s.nextDouble();

while(gradiente(u, r) > tol)

{

System.out.println(k + " " + r[0] + " " + r[1] + " " + f(r));

gradiente(u, r);

r[0] -= tol*u[0];

r[1] -= tol*u[1];

k ++;

}

}

public double f(double r[])

{

return r[0]*r[0] +2.0*r[0] + 3.0*r[1]*r[1];

}

public double gradiente(double u[], double r[])

{

double mag;

u[0] = 2.0*r[0] + 2.0;

u[1] = 6.0*r[1];

mag = Math.sqrt(u[0]*u[0] + u[1]*u[1]);

u[0] /= mag;

u[1] /= mag;

System.out.println("La Respuesta es: "+mag);

return mag;

}

}

MÉTODO DE NEWTON

package metodo_numerico_udo;

import java.util.Scanner;

public class Newton{

private Scanner s = new Scanner (System.in);

private double x0, tol;

private int nIter;

Newton(){

System.out.println("Ingrese Aproximacion: ");

x0=s.nextDouble();

System.out.println("Ingrese Tolerancia: ");

tol=s.nextDouble();

System.out.println("Ingrese No Iteraciones: ");

nIter=s.nextInt();

}

private double f(double x){

double y = (0.01*x + 1)*Math.sin(x)- (x - 0.01)/(Math.pow(x,2) + 1) - 0.0096;

return y;

}

public void calculaRaiz(){

double x = x0, xb = x-999;

double n = 0, del_x = 0.01;

while(Math.abs(x-xb)>tol){

n = n+1;

xb = x;

if(n > nIter) break;

double y = f(x);

double y_driv=(f(x+del_x) - y)/del_x;

x = xb - y/y_driv;

System.out.println(" n="+n+" x= "+x+" y = "+y);

// fprintf(' yd = %12.5e \n', y_driv)

}

System.out.println("La Respuesta es= "+ x);

}

}

MÉTODO DEL PUNTO FIJO

package metodo_numerico_udo;

...