Beyond some size of the transition matrix, my computer cannot cope with the Markov Chain problem I am working on (in MATLAB). However, I am sure I am not aware of all the useful tricks that can extend the size of what is possible.
What are some must-know algorithms for working with a very large transition matrix?
A little more specifically, I am working on a problem about the transitions of a group from state to state, where the current state is defined by the configuration of elements in the group (think 1's and 0's for each element, although the state of each element may be more refined) and the transition depends on how the elements in the group change (between 1 and 0 in the simplest case)
Since the combinatorics very quickly blows-up when the group contain many elements and when we move beyond the simple 1 and 0 possible element states, I am having a difficult time examining the behaviour of the group for anything but small groups and simple possible states of elements.
I would like to examine large system behaviour, and therefore I am asking for strategies to push the limits.
It may also be important to note that some states of the group are absorbing states (in which elements in the group stop changing).