Technical note: A successive over-relaxation preconditioner to solve mixed model equations for genetic evaluation.

A computationally efficient preconditioned conjugate gradient algorithm with a symmetric successive over-relaxation (SSOR) preconditioner for the iterative solution of set mixed model equations is described. The potential computational savings of this approach are examined for an example of single-step genomic evaluation of Australian sheep. Results show that the SSOR preconditioner can substantially reduce the number of iterates required for solutions to converge compared with simpler preconditioners with marked reductions in overall computing time.