Método Broyden
Publicado por titopuente (2 intervenciones) el 21/05/2012 18:08:14
Hola, alguien me puede proporcionar un código de matlab para resolver sistemas de ecuaciones no lineales por el método de Broyden. Buceando un poco por la red he encontrado este código, pero al meter el sistema de ecuaciones me decia q
function [xv,it]=broyden(x,f,n,tol)
% Broyden's method for solving a system of n non-linear equations
% in n variables.
%
% Example call: [xv,it]=broyden(x,f,n,tol)
% Requires an initial approximation column vector x. tol is required
% accuracy. User must define function f, for example see page 115.
% xv is the solution vector, parameter it is number of iterations
% taken. WARNING. Method may fail, for example, if initial estimates
% are poor.
%
fr=zeros(n,1); it=0; xv=x;
%Set initial Br
Br=eye(n);
fr=feval(f, xv);
while norm(fr)>tol
it=it+1;
pr=-Br*fr;
tau=1;
xv1=xv+tau*pr; xv=xv1;
oldfr=fr; fr=feval(f,xv);
%Update approximation to Jacobian using Broydens formula
y=fr-oldfr; oldBr=Br;
oyp=oldBr*y-pr; pB=pr'*oldBr;
for i=1:n
for j=1:n
M(i,j)=oyp(i)*pB(j);
end;
end;
Br=oldBr-M./(pr'*oldBr*y);
end;
function [xv,it]=broyden(x,f,n,tol)
% Broyden's method for solving a system of n non-linear equations
% in n variables.
%
% Example call: [xv,it]=broyden(x,f,n,tol)
% Requires an initial approximation column vector x. tol is required
% accuracy. User must define function f, for example see page 115.
% xv is the solution vector, parameter it is number of iterations
% taken. WARNING. Method may fail, for example, if initial estimates
% are poor.
%
fr=zeros(n,1); it=0; xv=x;
%Set initial Br
Br=eye(n);
fr=feval(f, xv);
while norm(fr)>tol
it=it+1;
pr=-Br*fr;
tau=1;
xv1=xv+tau*pr; xv=xv1;
oldfr=fr; fr=feval(f,xv);
%Update approximation to Jacobian using Broydens formula
y=fr-oldfr; oldBr=Br;
oyp=oldBr*y-pr; pB=pr'*oldBr;
for i=1:n
for j=1:n
M(i,j)=oyp(i)*pB(j);
end;
end;
Br=oldBr-M./(pr'*oldBr*y);
end;
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