Fast And Accurate Parallel Solutions for Recursive Least Squares Problems

本研究的目标是发展递归最小二乘问题快速准确的求解技术，并通过理论和实验研究对其进行分析。这些技术将基于精确的降年算法、快速旋转和鲁棒的到达方向估计算法。对全秩降期问题的初步研究表明，现有算法在稳定性和速度上存在较大差异。稳定性和复杂性分析将是改进算法的重要组成部分，算法开发将利用快速旋转和迭代细化等技术。研究结果将扩展到设计块算法，可以有效地同时处理多个更新和降级。虽然奇异值分解（SVD）对秩缺乏问题有很好的解，但是奇异值分解的计算和修改代价很大。该研究将扩展近年来发展起来的揭示秩的正交分解，为秩不足递推问题的快速求解提供了新的思路。研究结果将应用于新型自适应到达方向估计算法的设计，有望产生更快、更准确的算法。这些算法将在CM-5计算机上并行实现，以确定它们在实时应用中的实用价值。

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.