Solving large mixed linear models using preconditioned conjugate gradient iteration

Continuous evaluation of dairy cattle with a random regression test-day mod el requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using ite ration on data is presented. In the new computing technique, the calculatio ns in multiplication of a vector by a matrix were reordered to three steps instead of the commonly used two steps. The three-step method was implement ed in a general mixed linear model program that used preconditioned conjuga te gradient iteration. Performance of this program in comparison to other g eneral solving programs was assessed via estimation of breeding values usin g univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, a t best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at leas t 20 and 435% more time to solve the univariate and multivariate animal mod els, respectively. Computations of the second best iteration on data took a pproximately three and five times longer for the animal and test-day models , respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large bre eding value problems is supported by our findings.