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

复杂随机系统的马尔可夫链模型通常 其特征在于大的统计空间，导致计算 数值解的困难。 秩减少 算法通过分解来缓解大规模的不经济性 将给定问题分解为一组较小的子系统。 这项工作 便于实现各种迭代降秩 算法的效率和可用性。 这项工作的一个主要贡献是发展了 将大状态空间分解为小状态空间的启发式方法 子集 主要方法是基于对个体的分析 错误. 科学家和工程师试图分析复杂的 随机系统将受益于强大的， 用户友好的方法，如在这项工作中开发的方法。

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.