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.
