# Root Convergence rate of Iterative Scheme [closed]

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.

-

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

Questions on Mathematics Stack Exchange are expected to relate to math within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

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