Mathematical Sciences: Matrix Methods in the Mathematical Sciences

8902121 迈耶/普莱蒙斯 该项目涉及调查几个 数值线性代数中的问题，特别强调 递归最小二乘的并行算法 以及大尺度平稳分布的计算 马尔可夫链 递归最小二乘计算，包括 更新和降级算法在以下方面尤其重要： 信号处理和控制。 马尔可夫链具有广泛的 适用性作为模型的许多问题，在工程和 数学和物理科学。 更多努力 将在研究稳定性和调节 与递归最小二乘和马尔可夫相关的问题 链计算和更一般的特征向量问题。 一个 这项研究的建筑方面将涉及 确定当代和拟议的 多处理器，最适合实现 正在调查的算法。 本研究的目的是调查 这些计算的理论方面，以及发展 解决大规模问题的新技术 高效稳定的方式。

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.