programas de metodos numericos.docx

8/11/2019 programas de metodos numericos.docx

1/9

functiony=f(x)y=x+lnx;

Mtodo de la biseccionfunction[c,k]=biseccion(a,b,t)k=0;c=(a+b)/2;whileb-a>=t & f(c)~=0

iff(a)*f(c)0

disp('elija otros puntos')return

endfprintf('\n k | a b c error \n')fori=1:ceil(n)+1

c=(a+b)/2;e=abs(b-a);fprintf('%3d | %5.6f |%5.6f |%5.6f |%5.6f |\n',i-1,a,b,c,e)iff(a)*f(c)=e && abs(f(c))>=e

iff(c)==0break;

endiff(a)*f(c)


2/9

elsea=c;

endk=k+1;c=[(f(a)*b)-(f(b)*a)]/(f(a)-f(b));

endend

functiony=f(x)y=x+lnx;

Mtodo de newtonfunction[x,iter]=newton2(x0,f,df)% Algoritmo Newton-RaphsonN = 100; eps = 1.e-5; %Defino max. Numero. iteraciones y errormaxval = 10000.0; % Defino valor para divergenciax=x0;while(N>0)

xn = x-f(x)/df(x);%Funcin de Newtonifabs(f(xn))maxval

disp(['# de Iteraciones = ',num2str(iter)]);error('La Solucion Diverge');break;

end;N = N - 1;x = xn;

end;error('No Converge');return;% Fin de la Funcion


3/9

function[x,k]=newton(x,t1,t2)k=0; y=x+1;whileabs(f(x))>=t1 & abs(y-x)>=t2

y=x;x=x-f(x)/df(x);k=k+1;ifk>10000

break;end

functionNewton3(f,x,tol)disp('=========METODO DE NEWTON=========')g=diff(f);c='x'-f/g;%fprintf('g(x)=%c',pretty(c)')%pretty(c);f=inline(f);

c=inline(c);g=inline(g);k=-1;ifg(x)==0

disp('Dar otro valo inicial')return

endfprintf('\n k | x g(x) error\n')disp('-------------------------------------------')while1


4/9

Falsa posicionfunctionfalsaposicion1 (f,a,b,tol)f=inline(f);iff(a)*f(b)tol

c=b-(f(b)*(b-a)/(f(b)-f(a));fprintf('\n % 3d %5.7f %5.7f\n',I,a,b,c);ifI>100

break;endiff(a)*f(c)=e

c=[(f(a)*b)-(f(b)*a)]/(f(a)-f(b));iff(c)==0

break;endiff(a)*f(c)


5/9

iff(a)*f(b)tol

c=b-(f(b)*(b-a)/(f(b)-f(a));fprintf('\n % 3d %5.7f %5.7f\n',I,a,b,c);ifI>100

break;endiff(a)*f(c)


6/9

punto fijofunctionpuntofijo1(g,x,tol)g=inline(g);k=-1;disp('=======Metodo del punto fijo=======')fprintf(' k | x | g(x) | error |\n')disp('------------')while5


7/9

Secantefunction[x1,k]=secante(x0,x1,t1,t2)k=0;

whileabs(f(x1))>=t1 & abs(x1-x0)>=t2aux=x1;x1=x1-(f(x1)*(x1-x0))/(f(x1)-f(x0));x0=aux;k=k+1;

end

function[x1,k]=secantemed(x0,x1,t1,t2)k=0;whileabs(f(x1))>=t1 & abs(x1-x0)>=t2

aux=x1;x1=x1-(f(x1)*(x1-x0))/(f(x1)-f(x0));x0=aux;k=k+1;ifk>1000

error('parece que no converge');end

end


8/9

Sistema lineales

%matrizA=[5 -8 9 11;0 2 -7 13;0 0 1 17;0 0 0 9 ]B=[1 -2 30 -8

Gauss

functionx=GAUSS(A,B)[m,n]=size(A);fork=1:n

fori=k+1:nz=A(i,k)/A(k,k);

A(i,k)=0;forj=k+1:n

A(i,j)=A(i,j)-z*A(k,j);

endB(i)=B(i)-z*B(k);end

enddisp(A);x=zeros(n,1);x(n)=B(n)/A(n,n);fork=n-1:-1:1

s=0;forj=k+1:n

s=s+A(k,j)*x(j);endx(k)=(B(k)-s)/A(k,k);

end


9/9

Solucin de un sistema triangular superior

functionx=RSTS(A,b)[m,n]=size(A);x=zeros(n,1);

x(n)=b(n)/A(n,n);fork=n-1:-1:1s=0;forj=k+1:n

s=s+A(k,j)*x(j);endx(k)=(b(k)-s)/A(k,k);

end

programas de metodos numericos.docx

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