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From Jonathan Richard Shewchuk:

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By using equation (13), we have lost track of $x_(i)$ in the process of iteration. How is it possible to recompute the correct residual using equation (10) ever again?

qed
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1 Answers1

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Of course, the algorithm computes both $x_i$ and $r_i$ in each step. The calculation (13) is only done to save one additional matrix vector multiplication: $Ar_i$ has to be computed to get the step size $\alpha_i$.

daw
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