It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing...