How do I count how many iterations my root is in a smaller interval?

Question

Matthew Worker 2017-11-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/366444-how-do-i-count-how-many-iterations-my-root-is-in-a-smaller-interval

编辑： Rena Berman 2018-3-21

In my code I need to display in the command line how many of the iterations my root was in the smaller interval. I am not entirely sure what this means, but I'm hoping someone does and can give me a hand to work out what I'm missing. At the moment the command line displays the same number of iterations for both the iterations to the root and how many iterations the root was in the smaller interval.

Code removed. Question has been answered.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Mischa Kim 2017-11-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/366444-how-do-i-count-how-many-iterations-my-root-is-in-a-smaller-interval#answer_290562

In each iteration you have two intervals, [a,c] and [c,b]. Compute the size of both intervals and use the last if-else condition in your code to increment itc.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Mischa Kim 2017-11-11

在 MATLAB Online 中打开

I used

 f = @(x) sqrt(x) - cos(x);
 [a,b,it,itc] = WB(f,0,15,0.25,1e-5)

with (please double-check)

function [a,b,it,itc] = WB(f,a,b,w,tol)
it=0;
itc=0;
fa=f(a);
fb=f(b);
if fa*fb>0
    error('Not guaranteed a root in interval [a,b]');
end
if abs(fa)<abs(fb)
    fprintf('The root is probably closer to a than b\n');
else
    abs(fa)>abs(fb);
    fprintf('The root is probably closer to b than a\n');
end
while (b-a)/2>tol
    c  = (1-w)*a+w*b;
%     fc = f(c);    % not really needed
%     if fc == 0
%         return
%     end
    x = abs(a-c);
    y = abs(c-b);
    if f(a)*f(c)<0
        b = c;
        if x<y
            itc = itc + 1;
        end
    else
        a = c;
        if y<x
            itc = itc + 1;
        end
    end
    it = it+1;
end
fprintf('Final interval: [%f, %f] with %d iterations and %d iterations where the root was in the smaller interval\n',a,b,it,itc)
end