This is a small part of a much larger question to do with optimization but is the only part I cant get!
Apply Newton's method (without linesearch) to minimize the univariate function,
, ,
starting from and let be the generated sequence of iterates.
Prove that the limit points of the sequence of iterates are +1 and -1 as .
This is the sequence...
And Newtons method is...
So how would I do this. Some examples in class just had the sequence of iterates with the statement "clearly the sequence converges to ..." but I think I should be giving a proper proof.