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I have an iterative sequence for optimizing an EM algorithm based loss function $L(X)$ with $t$ being the iteration number as: $X_t=ABX_{t-1}+CX_{t-1}+X_{t-1}$ where $A$ is a diagonal matrix, $B$ and $C$ are positive semi-definite matrices. Also the diagonal entries in $A$ are the inverse of the diagonal elements of $C$. i.e, $A=Diag^{-1}(C)$.

I would like to compute the convergence rate (root-convergence rate) of this algorithm as $t\to \infty$. Am assuming it has got to do with taylor expansions, spectral radii and fixed point theorems. How is this approached or done for iterative schemes?

Also- a notational doubt. What does $DG(.)$ mean in theorem 1.1(Ostrowski Theorem) in this paper by Deleeuw, Stat, UCLA: "Accelerating Majorization Algorithms" available at: http://escholarship.org/uc/item/41v9961m#page-1? This paper deals with convergence rates of iterative schemes based on spectral radii.

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closed as off topic by Did, sdcvvc, William, Matt N., t.b. Sep 11 '12 at 16:13

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Maybe this question is more suitable on scicomp.stackexchange.com? –  Shuhao Cao Aug 20 '12 at 22:32
Great. I was searching for a suitable SE site like math. Thanks for this pointer-it looks like a good avenue. –  user23600 Aug 20 '12 at 22:34
VSPCP This might not be quite explicit in the answer you received on the other site but at present there is every reason to suspect the algorithm you consider does not converge. Roughly speaking $I+C+AB\gt I$... –  Did Aug 27 '12 at 16:37