We present an equivalent equation system for solving single-step genomic BLUP that does not require separate forming or inversion of the pedigree relationship matrix of genotyped animals. The equation system is contrasted with original single-step equations and two augmented equation systems. Comparison was based on a small data having 73,579 animals of which 2,885 were genotyped. Number of unknowns to solve was 73,580, 79,350, 76,465 and 144,274 by original, full augmented, partly augmented, and our approach, respectively. Numbers of non-zeros in the coefficient matrix were c. 8.9, 12.9, 12.9, and 9.2 million, respectively. Hence, our approach increased substantially number of unknowns but the coefficient matrix remained sparse. Our equivalent system needed more iterations than the original single-step but was competitive with the augmentation methods.
Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume Genetic Improvement Programs: Selection using molecular information, , 069, 2014
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