Transformed Mixed Model Equations: A Recursive Algorithm to Eliminate A−1

Abstract

For Henderson's L defined such that LL′ = A, a numerator relationship matrix, a recursive algorithm is derived to overwrite a matrix B with L′B or, for square B, with L′BL working directly from a list of sires and dams (or maternal grandsires). The matrix L is never computed. Matrices so formed have application in procedures that use mixed model equations for estimating variance components. © 1989, American Dairy Science Association. All rights reserved.