Mathematical Sciences: Stochastic Matrix Analysis

首席研究员研究理论和 涉及马尔可夫链的随机计算问题 矩阵及其应用。 他研究了 随机矩阵Perron特征向量，发展了有效的 计算特征向量的方法，并研究了 随机矩阵及其相关的马尔可夫链。 计算方法包括适于并行计算的算法。 处理器. 随机矩阵和马尔可夫链 自然地，在各种各样的问题中， 工程、经济、运筹学和 自然科学和社会科学-例如，在计量经济学中， 模型和调度问题，其中客户端被服务 以随机的方式到达。 当铸造成一个系统的形式时， 方程，许多这样的问题具有对应于 系统的特征向量。

The principal investigator studies theoretical and computational problems involving Markov chains, stochastic matrices, and their applications. He examines the sensitivity of the Perron eigenvector of a stochastic matrix, develops efficient methods to compute that eigenvector, and studies the structure of stochastic matrices and their related Markov chains. Computational methods include algorithms suitable for parallel processors. Stochastic matrices and Markov chains arise naturally in the formulation of problems in a broad variety of areas in engineering, economics, operations research, and the physical and social sciences -- for example, in econometric models and in scheduling problems where the clients to be served arrive in random fashion. When cast in the form of a system of equations, many such problems have features that correspond to the eigenvectors of the system.