RECURSIVE LEAST-SQUARES ON A HYPERCUBE MULTIPROCESSOR USING THE CONVARIANCE FACTORIZATION

An efficient parallel implementation of an algorithm for recursive least squares computations based upon the covariance updating method has been developed. The target architecture is a distributed-memory multiprocessor, and test results on an Intel iPSC/2 hypercube demonstrate the parallel efficiency of the algorithm. A 64-node system is measured to execute the algorithm over 48 times as fast as a single processor for the largest problem that fits on a single node (fixed-size speedup). Moreover, the computation times increase only slightly with an increase in the number of processors when the problem size per processor remains constant. Applications include robust regression in statistics and modification of the Hessian matrix in optimization, but the primary motivation for this work is the need for fast recursive least squares computations in adaptive filtering methods in signal processing.