Determine if valid initial guess for closed numerical method

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If I'm given a function f(x), how can I determine whether say [0 1] or [1,2 ] are valid initial guesses for a closed numerical method, of solving f(x)=0.

Answers (1)

Torsten
Torsten on 21 Feb 2018
Edited: Torsten on 21 Feb 2018
If you want to use "fzero", you can first evaluate f in the endpoints of the interval [a b] you provide. If sign(f(a)*f(b)) < 0, you provide a valid initial guess.
Or did you want to ask something else - because your question was quite unclear ?
Best wishes
Torsten.
  4 Comments
Rachel Dawn
Rachel Dawn on 21 Feb 2018
Also, sorry for all the questions, but in the following code:
while(iteration <=100 && abs(xleft-xright)>10^-3
it's part of the bisection method, but what does that abs part imply? why is it necessary?
Torsten
Torsten on 22 Feb 2018
Try
xa = 10;
xb = 21;
fxa = f(xa);
fxb = f(xb);
if fxa*fxb > 0
disp('Invalid initial guess.')
end
iteration = 1;
E = 0.1;
error_f = 1.0;
while (iteration < 100 && error_f >= E)
xc = (xa+xb)/2;
fxc = f(xc);
if fxc*fxa<0
xb = xc;
else
xa = xc;
fxa = fxc;
end
error_f = abs(fxc);
iteration = iteration+1;
end
xc
You do not need to include the abs-part from above in the while-statement because the number of iterations already determines the minimum length of the interval in which you search for the root.
Best wishes
Torsten.

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