Infinite loop in False postion method

Question

R Abhinandan 2020-10-27

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https://ww2.mathworks.cn/matlabcentral/answers/628068-infinite-loop-in-false-postion-method

评论： Cris LaPierre 2020-10-27

Here is my code for false position method and im getting a infinite loop, i want it to stop at tol=10^-4, can someone help?

a=0.5;
b=1;
tol=0.0001;
counter=0;
f =@(x) exp(x)-3*x^2;
while abs(b-a)>tol 
c= b - (f(b)* (b-a)/(f(b)-f(a)));
if f(a)*f(c)<0 
    b=c;
end
if f(a)*f(c)>0
    a=c;
end
counter=counter+1;
er=abs(a-b);
errorcounter(counter)=er; 
end
figure
hold on
plot(errorcounter)
title('Convergence of False Position')
ylabel('Error')
xlabel('Iterations')
axis ([0 5 0 9e-04])

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Cris LaPierre 2020-10-27

btw, hold on is unnecessary here. When used, it should always be paired with hold off.

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Answer 1

Cris LaPierre 2020-10-27

0
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在 MATLAB Online 中打开

I don't understand what your approach is, but by converting your while loop to a for loop, I can see that your error stops decreasing at 0.09. Here's a simplified version of your code.

a=0.5;
b=1;
f =@(x) exp(x)-3*x^2;
% while abs(b-a)>tol 
for loop = 1:10
    c= b - (f(b)* (b-a)/(f(b)-f(a)));
    if f(a)*f(c)<0 
        b=c;
    elseif f(a)*f(c)>0
        a=c;
    end
    er=abs(a-b)
end
er = 0.1193
er = 0.0915
er = 0.0901
er = 0.0900
er = 0.0900
er = 0.0900
er = 0.0900
er = 0.0900
er = 0.0900
er = 0.0900

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R Abhinandan 2020-10-27

在 MATLAB Online 中打开

I want the loop to stop at tol=10^-4, for example here is my code for bisection method which works perfectly but when i tried for false postion it doesn't

 f=@(x) exp(x)-3*(x)^2;
 a=0.5;
 b=1;
 tol=10^(-4);
 counter = 0; 
while abs(b-a) > tol 
   c = (b+a)/2; 
    if (f(a)*f(c)) <0 
        b = c;
    end
    if (f(a)*f(c)) >0 
        a = c; 
    end
   counter = counter + 1;
   err(counter) = abs(a - b);
end
disp(b)
figure
hold on
plot(err)
title('Convergence of Bisection')
ylabel('Error')
xlabel('Iterations')
axis ([0 13 0 0.0001])