A VLSI array for stable matrix inversion using gauss-jordan diagonalization

Abstract

A purely systolic architecture for computing the inverse of a matrix has been presented. The architecture implements an inversion algorithm based on the Gauss-Jordan diagonalization method with partial pivoting. The architecture employs 4n+1 PEs and has a time complexity of O(n²). Thus the area-time complexity is O(n³), which matches the performance of the fastest systolic implementation of matrix inversion (numerically unstable in most cases), reported to date.

A regular and continuous data flow is maintained within the array. The bilinear array has been supplemented with a buffer array to eliminate the need for costly inter-iteration I/O. Thus, the total number of I/O operations has been minimized and I/O operations are needed only to input the matrix to be inverted and to retrieve its inverse.