Technical Abstract: Efficient methods for processing genomic data were developed to increase reliability of estimated breeding values and simultaneously estimate thousands of marker effects. Algorithms were derived and computer programs tested on simulated data for 50,000 markers and 2,967 bulls. Accurate estimates of allele frequencies in the base population were essential in estimating genomic inbreeding coefficients. Linear model predictions of breeding value were computed by 3 equivalent methods: 1) selection index including a genomic relationship matrix, 2) mixed model equations including inverse of genomic relationships, and 3) iteration for individual allele effects followed by summation across loci to obtain estimated breeding values. A blend of first- and second-order Jacobi iteration using 2 separate relaxation factors converged well for allele frequencies and effects. Tested genomic predictions required only a few days of computing. Reliability of predicted net merit for young bulls was 63% as compared with 32% using the traditional relationship matrix. Nonlinear predictions were also computed using iteration on data and nonlinear regression on marker deviations; an additional (about 3%) gain in reliability for young bulls resulted in a mean reliability of 66%. Information from genotyping was equivalent to about 20 daughters with phenotypic records. Actual gains may differ because the simulation did not account for linkage disequilibrium in the base population or selection in subsequent generations.