Comparison of different solving strategies in multiple-trait mixed model equations with iterative algorithms

Abstract

The effects of initial solution and order of observations on the solving of mixed model equations (MME) by traditional iterative algorithms-Gauss-Seidel, successive over-relaxation (SOR), and second-order Jacobi-and by preconditioned conjugate gradient algorithms-scaled conjugate gradient (SCG) and incomplete Cholesky conjugate gradient (ICCG) simulation were investigated by using data in a computer. With SOR, the use of adjusted initial solutions based on phenotype and heritability of the trait and order of the animal within the trait in the MME was effective for fast convergence. Adjustment of initial solutions was not an advantage in preconditioned conjugate gradient algorithms. Of the five algorithms, ICCG required the lowest number of iterations until convergence. However, ICCG needed the largest central processing unit (CPU) time to calculate one round of iteration. The SCG algorithm was an attractive alternative for solving MME because it required the second fewest rounds of iteration and had the shortest CPU time per round of iteration until convergence.