Systolic rank updating and the solution of non-linear equations

A systolic array for performing rank-m updates to a given matrix whose inverse is known using the Sherman-Morrison-Woodbury formula is presented. The array can perform a rank-m update of an n×n matrix in 6n+3m steps which includes input and output time and requires O(n²+m²) cells. The design computes in three phases consisting of two pipelined Faddeev operations to compute the Schur complement of a particular matrix. Each phase is pipelined and overlapped with the others to provide high throughput. An extension to the basic array is given which shows how the feedback can be used to solve nonlinear equations using the Quasi-Newton Broyden algorithm