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Question 7.E.3.16: Let H = (1 0 0 −1 −2 −1 0 2 1). (a) Apply the “vanilla” QR i......

Let H = \begin{pmatrix}1 &0& 0\\ −1 &−2 &−1\\ 0 &2& 1\end{pmatrix}.

(a) Apply the “vanilla” QR iteration to H.

(b) Apply the the single shift QR iteration on H.

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(a) The “vanilla” QR iteration fails to converge.

(b) H  −  I = QR = \begin{pmatrix}0 &0 &1\\ −1 &0& 0\\ 0 &1& 0\end{pmatrix} \begin{pmatrix}1 &3& 1\\ 0 &2& 0\\ 0 &0& 0\end{pmatrix}  and  RQ + I = \begin{pmatrix}−2& 1 &1\\ −2 &1& 0\\ 0 &0& 1\end{pmatrix}.

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