# Root Convergence Rate of EM or MM Iteration [closed]

I have an iterative sequence for optimizing an EM/MM 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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I think this question would find a more interested readership on one of the SE sites related to mathematics or computing. –  whuber Aug 20 '12 at 22:12
Did a search and found scicomp.stackexchange.com to be a good avenue apart from the math SE. –  PraneethVepakomma Aug 20 '12 at 22:40
Cross-posted at stats.stackexchange.com/questions/34745/…. –  whuber Aug 21 '12 at 15:15