An estimate of the absolute value and width of the solution of a linear system of equations with tridiagonal interval matrix by the interval sweep method

We consider linear systems of algebraic equations Su = f with tridiagonal interval matrix S and interval vector f An interval version of the sweep method allows us to find an interval vector u = ( u t , u 2 , . . . , u n ) T that contains the united set of solutions of the system. In the paper we present estimates of the absolute value and the width of the intervals ui, i = 1, 2 , . . . , ~z tinder certain assumptions on the elements of the matrix S that do not include the traditional condition of diagonal dominance. The width estimates are three orders of magnitude narrnwer, and the assumptions on the system's coefficients are weaker than those in works published so far.