编辑牛顿方法代码以包括终止条件

问题描述

function [ sol,flag ] = newtonx(sx,relerr,maxit,func)
% [SOL,FLAG]=NEWTONX(SX,RELERR,MAXIT,FUNC)
%
% Solves f(x)=0 using Newton’s method
%
% Input: scalar sx - starting point of the iteration
%        small positive scalar relerr - desired relative error
%        positive integer maxit - maximum no. of iterations permitted
%        func: name of the program that defines f(x);
%
%        Note: when running newtonx on the problem defined by func,you
%        must enter @func (func with symbol @ attached) in the input line.
%        The calling sequence for the program func must have the format
%               [yval,yder]=func(x)
%        where x is the point used to compute yval=f(x) and yder=f’(x).
%
% Output: scalar sol - solution found
%        scalar flag - flag=0 indicates solution successfully found
%                     flag=1 indicates derivative too small; halt
%                     flag=2 indicates too many iterations; halt
k=0 ;
while (k<maxit)
    k=k+1 ;
    [yval,yder]=func(sx) ; % evaluate f(x) and f’(x)
    if (abs(yder)<abs(yval)*sqrt(eps))
        sol=[]; flag=1 ; return % derivative too small
    end
    sx = sx - yval / yder ; % take the Newton step
    if (relerr == 0)
        sol=sx ; flag=0 ; return % succesful termination
    end
end
sol=[]; flag=2 ; % failure: too many steps
end

我需要有关合适的终止标准的帮助，目前，我有（relerr == 0），但我确定这是不正确的。任何帮助或提示都很棒，我不确定该怎么办。

解决方法

| sx-sx_ {上一页} | = | yval / yder |

因此，相对误差公式为| yval /（sx * yder）|或在matlab术语中为abs（yval /（sx * yder））

abs（yval /（sx * yder））