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 grand-sires). The matrix L is never computed. Matrices so formed have application in procedures that use mixed model equations for estimating variance components