= Truncated Tikhonov resolvent
{title2=$R_{\alpha,2}=\alpha^{-1}I-\alpha^{-2}B+\alpha^{-3}B^2$}
For $B=AA^*\ge0$, the polynomial displayed here truncates the <Neumann series> for $(\alpha I+B)^{-1}$. It obeys $(\alpha I+B)R_{\alpha,2}=I+\alpha^{-3}B^3$, and is not an exact inverse. If $\|B\|/\alpha<1$, it is a controlled large-parameter expansion; its error is $\alpha^{-3}B^3(\alpha I+B)^{-1}$. At each fixed positive parameter the reconstruction $A^*R_{\alpha,2}$ is bounded. However this polynomial diverges on nonzero singular modes as $\alpha\to0$ and is not a substitute for the exact convergent Tikhonov filter in that limit.
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