newton.m

来自「sareli<matlab科学计算>配套程序」· M 代码 · 共 33 行

function [zero,res,niter]=newton(f,df,x0,tol,nmax,varargin)
%NEWTON Find function zeros.
%   ZERO=NEWTON(FUN,DFUN,X0,TOL,NMAX) tries to find the zero ZERO of the 
%   continuous and differentiable function FUN nearest to X0 using the Newton 
%   method. FUN and its derivative DFUN accept real scalar input x and returns 
%   a real scalar value. If the search fails an errore message is displayed.
%   FUN and DFUN can also be inline objects.
%
%   [ZERO,RES,NITER]= NEWTON(FUN,...) returns the value of the residual in ZERO
%   and the iteration number at which ZERO was computed.

x = x0; 
fx = feval(f,x,varargin{:}); 
dfx = feval(df,x,varargin{:});
niter = 0; 
diff = tol+1;
while diff >= tol & niter <= nmax
   niter = niter + 1;
   diff = - fx/dfx;
   x = x + diff;     
   diff = abs(diff);
   fx = feval(f,x,varargin{:});        
   dfx = feval(df,x,varargin{:});
end
if niter > nmax
    fprintf(['newton stopped without converging to the desired tolerance',...
    'because the maximum number of iterations was reached\n']);
    varargin{:}
end
zero = x;
res = fx;

return