Genomic selection is the term used for all methods and techniques that allow to predict the (future) agronomic performance of a plant or animal from its dense molecular fingerprint. This project aims to develop and implement a genomic prediction methodology that is applicable on an industrial scale. Reproducing Kernel Hilbert Space (RKHS) regression kernels are to be integrated in a linear mixed model framework which allows the estimation of missing kernel- and variance parameters by means of Restricted Maximum Likelihood (REML). The resulting system of linear equations is sparse but contains one or more dense kernels which implies that obtaining the solution requires a combination of specifically adapted solving routines. Furthermore, these routines should allow to distribute the workload over the nodes of a computer cluster. This approach allows to use all available genetic and phenotypic data of an entire breeding program to construct an accurate genomic prediction model for one or more economically relevant traits. The goal is to implement the developed methods in a computationally efficient and user- friendly software package that is to be commercialized by a dedicated spin-off company.