On fixed-point implementation of symmetric matrix inversion

Abstract

In this work we explore the trade-offs between established algorithms for symmetric matrix inversion for fixed-point hardware implementation. Inversion of symmetric positive definite matrices finds applications in many areas, e.g. in MIMO detection and adaptive filtering. We explore computational complexity and show simulation results where numerical properties are analyzed. We show that LDLT decomposition combined with equation system solving are the most promising algorithm for fixed-point hardware implementation. We further show that simply counting the number of operations does not establish a valid comparison between the algorithms as the required word lengths differ significantly.