02314naa a2200169 a 450000100080000000500110000800800410001910000160006024500740007626000090015030000190015952018660017865000110204465000140205570000160206977300590208513138792026-01-30       2007    bl uuuu     u00u1 u    #d1 aLEGARRA, A.  aComputing strategies in genome-wide selection.h[electronic resource]  c2007  cTechnical note  aGenome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving.  aGenoma  aSeleção1 aMISZTAL, I.  tJournal of Dairy Sciencegv. 91, n. 1. p 360-366, 2007