Research Initiation: Developing Heuristics for Rank Reduction Algorithms for Large-Scale Markov Chains

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Markov chain models of complex stochastic systems are often characterized by large stat spaces, resulting in computational difficulties in their numerical solution. Rank reduction algorithms alleviate the diseconomies of large\scale by decomposing the given problem into a set of smaller subsystems. This work facilitates the implementations of various iterative rank reduction algorithms with respect to efficiency and usability. A major contribution of this work is the development of heuristic methods for decomposing large state of spaces into small subsets. The main approach is based on analyzing individual errors. Scientists and engineers attempting to analyze complex stochastic systems will benefit from the availability of powerful, user friendly methods such as the ones developed in this work.