Fast Reliable Algorithms for Structured Computations

用于结构化计算的快速可靠的算法

• 批准号: 9732376
• 负责人: Ali Sayed
• 金额: $ 15.23万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732376&HistoricalAwards=false
• 关键词: Fast; Reliable; Algorithms; Structured; Computations

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.

该项目涉及计算算法的设计，该算法将结构矩阵问题的效率和数值精度的实际优点融合在一起。 速度和精度这两个要求通常被认为是相互竞争的，因此，为大规模结构化线性矩阵方程设计快速且数值可靠的算法在许多情况下仍然是一个重要的悬而未决的问题。 结构化矩阵方程出现在滤波、估计和控制领域的多种应用中。 这样，所提出的工作结果将进一步在解决这些领域中理论发现与实际结果之间一直存在的一些恼人的差异方面发挥具体作用。 这些差异通常是由于有限精度实现的缺陷造成的，特别是在涉及数字和模拟组件互连的系统中，而解决或改善其中许多困难的研究早就应该进行了。 这项研究将解决将数值精度和结构开发技术结合到统一框架中的挑战。 该项目将建立在最近完成的工作的基础上，将结果和框架扩展到更广泛的结构化矩阵问题，并将探索在过滤、估计和控制方面的应用。