### Questions 30 and 32, exam 2018

Hi, I have some questions concerning the 2018 exam.

For question 30, I can easily show that $$\Delta x_t = M\Delta y_t$$ if $$\Delta x_t$$ and $$\Delta y_t$$ are the Newton steps of the t-th iteration for g and h respectively, and not h and g. Is it an error, or is there something that I did not understand ?

For question 32, from the question 31 and the fact that $$||Ax-b||^2 = || A ( x-y ) + Ay - b ||^2$$, I find the same equation as in the statement but with a factor 1/2 for $$||Ax-b||^2$$ and $$||Ay-b||^2$$. Thus it comes to my mind that this is actually $$f(x) = 1/2 ||Ax-b||^2$$ (note the factor 1/2) that is smooth with the largest eigenvalue of A^TA as smoothing parameter.
An other way to see this is to compute the Hessian of $$f(x) = ||Ax-b||^2$$ , which is $$2A^TA$$, whose norm is bounded by 2 times the largest eigenvalue of $$A^TA$$. Where do I make any mistake ?

Top comment

Q30: Yes, y should be for h and x for g. It's a bit confusing, but you can check this at initialization.

Q32: Yes, you're right. Thanks for reporting.

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