Numerical accuracy control in fixed-point arithmetic

The purpose of this paper is to look at the problem of propagation of round-off errors in fixed-point arithmetic and at various problems of checking solutions of equations already treated by La Porte and Vignes in the case of floating-point arithmetic. We first consider the probabilistic model for the numerical fixed-point representation on a computer, the evaluation of the mean value and of the standard deviation for the absolute error of the assignment operator A, and of elementary operators of arithmetic. We then compute the statistical estimate of the error in the computation of an inner product, and this leads us to the problem of checking the accuracy of the solution of linear systems and of algebraic equations.