SOLVING ANIMAL-MODEL EQUATIONS THROUGH AN APPROXIMATE INCOMPLETE CHOLESKY DECOMPOSITION

A general strategy is described for the design of more efficient algorithms to solve the large linear systems Bs = r arising in (individual) animal model evaluations. This strategy, like Gauss-Seidel iteration, belongs to the family of "splitting methods" based on the decomposition B = B* + (B - B*), but, in contrast to other methods, it tries to take maximum advantage of the known sparsity structure of the mixed model coefficient matrix: B* is chosen to be an approximate incomplete Cholesky factor of B. The resulting procedure requires the solution of 2 triangular systems at each iteration and 2 readings of the data and pedigree file. This approach was applied to an animal model evaluation on 15 type traits and milking ease score from the French Holstein Association with 955 288 animals and 4 fixed effects, including group effect for animals with unknown parents. Its convergence was compared with a standard iterative procedure.