Array processing for linear system solutions

Processing elements are utilized for solving linear systems. One embodiment projects matrix elements along a diagonal of the matrix onto scalar processing elements to determine a Cholesky factor. Another embodiment uses a two-dimensional scalar array to determine a Cholesky factor. A third embodiment uses a reconfigurable scalar linear array to determine a Cholesky factor and perform forward and backward substitution. For matrices having a limited bandwidth, the processors used in these embodiments may be scaled down. Folding of the processors may be used to reduce the number of processors used in the embodiments. Another embodiment is a processing element capable of being reconfigured to determine a Cholesky factor and perform backward and forward substitution.