A statistical model of roundoff error for varying length floating-point arithmetic

A model is presented which explains the behavior of the roundoff error in a result quantity when computing precision is varied. A set of hypotheses concerning this a posteriori model is tested in a matrix inversion algorithm. The characteristics of the algorithms where the error model is valid are discussed. As an application of the model, the usual estimation procedure for roundoff error consisting of comparing the results computed in two different precisions is analyzed statistically.