This grant is in the area of adaptive signal processing which finds wide application in tailoring signal processing algorithms to current signal and noise characteristics, thus insuring best performance. Linear least squares prediction (LLSP) is widely used in adaptive speech processing to model the speech signal. In this application there is a need for the fast LLSP algorithms recently developed by Prof. Bojanczyk and others. This research is pursuing the development of these algorithms. The numerical stability of the fast LLSP algorithms is being studied. Modifications will be incorporated to improve stability while introducing only a modest overhead penalty. Also parallel algorithms suitable for systolic and hypercube architecture will be investigated. This grant is in the area of adaptive signal processing which finds wide application in tailoring signal processing algorithms to current signal and noise characteristics, thus insuring best performance. Linear least squares prediction (LLSP) is widely used in adaptive speech processing to model the speech signal. In this application there is a need for the fast LLSP algorithms recently developed by Prof. Bojanczyk and others. This research is pursuing the development of these algorithms.