Finite wordlength properties of matrix inversion algorithms in fixed-point and logarithmic number systems

Abstract

Matrix inversion is sensitive towards the number representation used. In this paper simulations of matrix inversion with numbers represented in the fixed-point and logarithmic number systems (LNS) are presented. A software framework has been implemented to allow extensive simulation of finite wordlength matrix inversion. Six different algorithms have been used and results on matrix condition number, wordlength, and to some extent matrix size are presented. The simulations among other things show that the wordlength requirements differ significantly between different algorithms in both fixed-point and LNS representations. The results can be used as a starting point for a matrix inversion hardware implementation.