Deflation techniques applied on mixed model equations

In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving sparse system of linear equations derived from statistical mixed model that analyses simultaneously phenotypic pedigree information genotyped ungenotyped animals with Single Polymorphism Nucleotide genotypes animals. livestock production systems, evaluating genetic merit through such is key process to ensure an improvement some characteristics interest at each generation. First, propose define vectors using subdomain approach considers biological properties genotypes. Using simulated data, reduces number iterations by up 87% comparison preconditioner. Furthermore, compared DPCG same subdomains but defined randomly, 20% computational costs one iteration. The resulting systems show annihilates largest eigenvalues preconditioned coefficient matrix. Second, use solution 12 include between 0.25% 3% less as vectors. For reducing costs, also Proper Orthogonal Decomposition-reduced set these recycling smallest matrix, results reduction 39% PCG method. Finally, based on our experiment, combination relying POD-based recycle previous vectors, defining annihilating both eigenvalues, 88 %