Fast Reliable Algorithms for Structured Computations

这个项目涉及的计算算法的设计，融合了效率和数值精度的矩阵问题的结构的实际优点。 这两个要求的速度和精度往往被认为是有竞争力的，因此，设计快速和数值可靠的算法，大规模结构化线性矩阵方程组在许多情况下仍然是一个重要的开放性问题。 结构化矩阵方程出现在滤波、估计和控制等学科的若干应用中。 这样，拟议工作的结果将进一步发挥具体作用，解决在这些领域理论研究结果与实际结果之间一直存在的一些令人讨厌的差异。 这些差异通常是由于有限精度实现的缺陷，特别是在涉及数字和模拟组件互连的系统中，解决或改善这些困难的研究早就应该进行了。 这项调查将解决的挑战相结合的数值精度和结构开发技术到一个统一的框架。 该项目将建立在最近完成的工作，将扩展的结果和框架，以更广泛的一类结构化矩阵问题，并将探讨在过滤，估计和控制的应用。

This project deals with the design of computational algorithms that blend together the practical virtues of efficiency and numerical accuracy for matrix problems with structure. The two requirements of speed and accuracy have often been regarded as competitive and, for this reason, the design of fast and numerically reliable algorithms for large-scale structured linear matrix equations has remained a significant open issue in many instances. Structured matrix equations arise in several applications in the disciplines of filtering, estimation, and control. In this way, the results of the proposed work will further play a concrete role in addressing some of the annoying discrepancies that have always existed in these areas between the theoretical findings and the practical results. These discrepancies are often due to the pitfalls of finite-precision implementations, especially in systems that involve interconnections of digital and analog components, and studies to resolve or ameliorate many of these difficulties have long been overdue. This investigation will address the challenge of combining numerical accuracy and structure exploiting techniques into a unifying framework. The project will build on the work recently done, will extend the results and the framework to a wider class of structured matrix problems, and will explore applications in filtering, estimation and control.