An efficient method of computing the numerator relationship matrix and its inverse matrix with inbreeding for large sets of animals

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Abstract
The numerator relationship matrix describes the genetic relationships between individuals of a population. Its inverse is used for the prediction of breeding values, as outlined by Henderson (1975a).For large populations, the recursive method commonly used is difficult to apply because of the size of the relationship matrix. Recently Henderson (1975b) derived a method which allows computing the inverse of the numerator relationship matrix itself for a large number of animals, provided the population is non-inbred. The method presented here is an extension of Henderson's method to allow for inbreeding with large number of animals. It takes inbreeding into account and computes the numerator relationship matrix as well as its inverse. The method is particularly efficient in computer storage in that it allows handling of sets of animals larger than 5000 animals, and is almost as fast as the recursive method.

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