- #1

mathmari

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MHB

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We have the matrix $\begin{pmatrix}2 & 1/2 & 1 \\ 1/2 & 3/2 & 1/2 \\ 1 & 1/2 & 2\end{pmatrix}$.

We take as initial approximation of $\lambda_2$ the $1.2$. We want to calculate this value approximately using the inverse iteration (2 steps) using as starting vector $x^{(0)}=\begin{pmatrix}1 \\ 1\\ 1\end{pmatrix}$.

At the inverse iteration method do we have to use at each step the Rayleigh-Quotient or only at the beginning and then just the power iteration ?

I think to get a better approximation that we have to use the Rayleigh-Quotient at each step. Is that correct?

:unsure: