Extrapolation and interpolation in line search optimization

[mathu2057]

hi
can you tell me these equations:

A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error
in MATLAB fmincg.m
https://github.com/emersonmoretto/mlclass-ex3/blob/master/fmincg.m
come from where??
it is either cubic interpolation or cubic interpolation...i look for
these equation in many website and books numerical optimization but
i do not find these equation even the book numerical optimization
for Peter Glynn Stephen M. Robinson p:57.(in the attachment copy of the page).it is not same in matlab
please help me from where these equation come from?

 

[jedishrfu]

From the MATLAB site I found some mention that they came from Coursera Machine Learning course taught by Andrew Ng.

https://www.mathworks.com/matlabcen...rization-used-to-classify-hand-written-digits

https://scicomp.stackexchange.com/questions/25876/understanding-matlabs-fmincg-optimization-function

In the code there is a test f2>f1 if true then a quadratic fit is done and if false then a cubit fit is done.

  if f2 > f1
    z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3);                 % quadratic fit
  else
    A = 6*(f2-f3)/z3+3*(d2+d3);                                 % cubic fit
    B = 3*(f3-f2)-z3*(d3+2*d2);
    z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A;       % numerical error possible - ok!
  end

so I think you will just have to go with the code and not worry about where it comes from. The code should be sufficient for you to decide why they are needed. Of course, there is always the distinct possibility that the code is wrong but again you will have to test and decide if that's the case.