Enhancing the scalability of selected inversion factorization algorithms in genomic prediction

A parallel distributed-memory approach for the exact calculation of selected entries of the inverse of a matrix arising in a Best Linear Unbiased Estimation (BLUE) problem in genomic prediction is presented. The particular structure of the matrices involved in this stochastic process, consisting of sparse and dense blocks, requires a framework coupling sparse and dense linear algebra algorithms. Our approach exploits direct sparse techniques based on the Takahashi equations, coupled with distributed LU dense factorizations and Schur-complement computations. The algorithm is validated on several matrices on a Cray XC40 supercomputer.