On an interval arithmetic and its applications

It is our point of view that familiar interval arithmetic defined by A∗B={a ∗ b: a ∊ A, b ∊ B}, ∗ ∊{+, −, ×, :} is inefficient in certain respects. For instance, it is not in a position to produce exact representations, of sets of the form {f(x, y, …, z):x ∊ X, y ∊ Y, …, z ∊ Z} even for simple functions f of one variable. We make use of another interval arithmetic which is very convenient for computer computations and for construction of interval algorithms. As an example we consider a method for the construction of interval expressions for sets of the form if {f(x):x ∊[x1, x2]}, where f is an elementary function.