2 Let Q R n n be symmetric and positive definite and letd 1 d2 dn Rn be a basis

2 let q r n n be symmetric and positive definite and

This preview shows page 3 - 4 out of 4 pages.

(2) LetQRn×nbe symmetric and positive definite, and letd1, d2, . . . , dnRnbe a basis ofQ-conjugate vectors. Show thatQ-1=nXi=1didTidTiQd(3) LetARm×nandbRm, and suppose that Nul(A) ={0}. Consider the functionf(x) :=12kAx-bk22.Show how to apply the CG algorithm to minimizefonRnunder the assumption thatAisnot available butAxcan be obtained for arbitrary vectorsxRn.
(4) Apply the conjugate gradient algorithm initialized atx0= (0,0,0)Tto solve the problemminxR312xTHx+gTx, whereH=210121012andg=311.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture