Mathematical Sciences: Matrix Methods in the Mathematical Sciences

[902121] Meyer/Plemmons本项目涉及数值线性代数中的几个问题的研究，特别强调递归最小二乘的并行算法和大规模马尔可夫链的平稳分布的计算。递归最小二乘计算，包括更新和降期算法，在信号处理和控制中尤为重要。马尔可夫链作为数学和物理科学中许多工程问题的模型具有广泛的适用性。我们将进一步努力研究与递归最小二乘和马尔可夫链计算以及更一般的特征向量问题相关的稳定性和条件问题。本研究的架构方面将涉及识别当代和拟议的多处理器的那些最适合实现所研究的算法的特征。本研究的目标是研究这些计算的理论方面，并开发新的技术，以高效和稳定的方式解决大规模问题。

8902121 Meyer/Plemmons This project involves the investigation of several problems in numerical linear algebra, with special emphasis on the topics of parallel algorithms for recursive least squares and the computation of stationary distributions for large scale Markov chains. Recursive least squares computations, including updating and downdating algorithms are especially important in signal processing and control. Markov chains have wide applicability as models for many problems in engineering and in the mathematical and physical sciences. Additional efforts will be made in the study of stability and conditioning problems associated with recursive least squares and Markov chain computations and more general eigenvector problems. An architectural aspect of this research will involve the identification of those features of contemporary and proposed multiprocessors which are best suited for implementing the algorithms under investigation. The goals of this research are to investigate the theoretical aspects of these computations as well as to develop new technologies for solving large scale problems in an efficient and stable way.