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Genet Mol Biol. 2010 Jan;33(1):198-204. doi: 10.1590/S1415-47572010005000014. Epub 2010 Mar 1.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection.

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  • 1Animal Breeding and Genetics Group, Department of Animal Science, Georg-August-University of Göttingen, Göttingen Germany.


The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use.


breeding value; genomic selection; mixed model equations; numerical method

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