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往往具有大的统计空间，这给其数值求解带来了计算上的困难。降阶算法通过将给定问题分解成一组较小的子系统来缓解大规模问题的不经济性。这项工作在效率和可用性方面促进了各种迭代降阶算法的实现。这项工作的一个主要贡献是发展了启发式方法，将大的空间状态分解成小的子集。主要方法是基于对个体错误的分析。试图分析复杂随机系统的科学家和工程师将受益于强大的、用户友好的方法的可用性，例如本工作中开发的方法。

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.