(i) Consider the rank one algorithm. Assume that H > 0. Show that if 6g(k) (5x(k)-Hg())>...

 

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(i) Consider the rank one algorithm. Assume that H > 0. Show that if 6g(k) (5x(k)-Hg())> 0, then H+1 > 0. (ii) Consider the DFP algorithm applied to the quadratic function 1 f(x)=xQx-xb, where Q Q> 0. (a) Write a formula for a in terms of Q, g(k), and d(). (b) Show that if g(k) 0, then a > 0. (i) Consider the rank one algorithm. Assume that H > 0. Show that if 6g(k) (5x(k)-Hg())> 0, then H+1 > 0. (ii) Consider the DFP algorithm applied to the quadratic function 1 f(x)=xQx-xb, where Q Q> 0. (a) Write a formula for a in terms of Q, g(k), and d(). (b) Show that if g(k) 0, then a > 0.