Previous reviews of signal processing computational needs and their systolic implementation have emphasized the need for a small set of matrix operations, primarily matrix multiplication, orthogonal triangularization, triangular backsolve, singular value decomposition, and the generalized singular value decomposition. Algorithms and architectures for these tasks are sufficiently well understood to begin transitioning from search to exploratory development. Substantial progress has also been reported on parallel algorithms for updating symmetric eigensystems and the singular value decomposition. Another problem which has proved to be easier than expected is inner product computation for high-speed high resolution predictive analog-to-digital conversion. Although inner product computation in a general setting will require Olog n time via a tree, the special structure of the prediction permits the use of a systolic transversal filter, producing a new predicted value in time O1. Problem areas which are still in an early of study include parallel algorithms for the Wigner-Ville Distribution function, L1 norm approximation, inequality constrained least squares, and the total least squares problem. Keywords Covariance matrix.