Indirect Solution of Mixed Model Equations

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Abstract
Large scale genetic evaluation of animals by best linear unbiased prediction can have a high computational cost. This is partly due to the need to set up mixed model equation, which are then solved in an iterative way. Solutions can also be obtained by successive averaging without setting the mixed model equations directly. Formulas are presented for a class of models with fixed and random factors, including an additive relationship matrix. Two iterative procedures were investigated, Gauss-Seidel and Jacobi. With a balanced data set, putting restrictions on fixed effects is not effective for improving convergence rates in GaussSeidel but is essential in Jacobi. Computational techniques needed to implement the indirect procedures are discussed.