Special Matrix Problems in Signals, Systems and Control

在过去的几十年里，线性代数发挥了重要作用。 在信号领域的进步中发挥着重要作用， 系统和控制。 最深刻的影响是在 计算和实施方面，其中数值线性 代数算法强烈地影响了 问题正在得到解决。 特殊计算的出现 诸如向量处理器和分布式处理器的体系结构 阵列还强调基本的并行和实时处理， 这些应用领域的线性代数模块。 这个项目是关于数值线性代数及其应用的 信号、系统和控制，特别强调 并行架构的实现方面。 重点是 “特殊矩阵”问题，即矩阵是稀疏的， 图案化或结构化。 对于这种矩阵，适当定义 最近引入了数值稳定性和灵敏度。 上述应用领域的数值方法应该是 在这种限制意义上的数值稳定，同时应该 利用矩阵的结构来提高计算效率， 复杂性和并行性。 这将适用于挑战 这些领域的问题，如目标跟踪，鲁棒控制， 大规模工厂的模型简化。

During the last few decades linear algebra has played a fundamental role in advances being made in the area of signals, systems and control. The most profound impact has been in the computational and implementational aspects, where numerical linear algebraic algorithms have strongly influenced the ways in which problems are being solved. The advent of special computing architectures such as vector processors and distributed processor arrays has also emphasized parallel and real-time processing of basic linear algebra modules for these application areas. This project is about numerical linear algebra and applications in signals, systems and control, with special emphasis on implementation aspects on parallel architectures. The focus is on "special matrix" problems, i.e. matrices which are either sparse, patterned or structured. For such matrices appropriate definitions of numerical stability and sensitivity have recently been introduced. Numerical methods for the above application areas ought to be numerically stable in this restricted sense and at the same time ought to exploit the structure of the matrices to improve computational complexity and parallelizability. This will be applied to challenging problems in these areas such as target tracking, robust control and model reduction of large scale plants.