Determine if valid initial guess for closed numerical method

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Rachel Dawn 2018-2-21

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评论： Torsten 2018-2-22

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.

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Torsten 2018-2-21

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编辑：Torsten 2018-2-21

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.

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Rachel Dawn 2018-2-21

在 MATLAB Online 中打开

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 2018-2-22

在 MATLAB Online 中打开

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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