Systolic rank updating and the solution of non-linear equations

摘要

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