Fast And Accurate Parallel Solutions for Recursive Least Squares Problems

这项研究的目标是发展快速和准确的 递归最小二乘问题的求解技术， 通过理论和实验研究分析。 这些技术将基于准确的下定日期 算法、快速旋转和鲁棒的到达方向 估计算法 对该事件的初步调查 满秩降级问题表明，现有的 算法在它们的稳定性和速度方面变化很大。 的 稳定性和复杂性分析将是 开发改进算法， 发展将利用技术，如快速旋转， 迭代精化 研究结果将推广到设计中 可以有效处理多次更新的块算法 同时也在降级。 虽然奇异值 分解（SVD）产生了很好的解决方案， 缺乏的问题，这是昂贵的计算和修改 SVD. 该研究将扩展最近开发的等级 揭示了正交分解，它可以提供快速 解决秩亏递归问题。 结果 将应用于新型自适应定向器的设计， 到达估计算法，预计将产生 更快更准确的算法 平行 这些算法的实现将在CM-5上进行 计算机建立他们的实用价值在真实的时间 应用.

The goal of this research is to develop fast and accurate solution techniques for recursive least squares problems and analyze them through theoretical and experimental studies. These techniques will be based on accurate downdating algorithms, fast rotations, and robust direction-of-arrival estimation algorithms. The preliminary investigations on the full rank downdating problems show that the existing algorithms vary greatly in their stability and speed. The stability and complexity analysis will be an essential part in developing the improved algorithms and the algorithm development will utilize techniques such as fast rotations and iterative refinement. The results will be extended to design block algorithms that can efficiently handle multiple updating and downdating simultaneously. Although the singular value decomposition (SVD) produces excellent solutions for rank deficient problems, it is costly to calculate and modify the SVD. The research will extend the recently developed rank revealing orthogonal decomposition, which can provide fast solutions to rank deficient recursive problems. The results will be applied to the design of novel adaptive direction-of- arrival estimation algorithms, which are expected to produce significantly faster and accurate algorithms. Parallel implementation of the algorithms will be conducted on the CM-5 computer to establish their practical values in real time applications.