On Optimal Solution of Interval Linear Equations

For interval linear algebraic systems Ax = b, we consider the problem of component-wise evaluation of the set Σ ∃ ∃ ( A, b) = \ A- 1 b A ∈ A,b ∈ b \ formed by all solutions of $Ax = b$ when A and b vary independently in A and b, respectively. An iterative PSS algorithm is introduced that computes optimal (exact) componentwise estimates of Σ ∃ ∃ and its convergence is proved under fairly general conditions on the interval system. We introduce the concept of a sequentially guaranteeing algorithm as a reasonable compromise between the requirements for the interval result to be guaranteed and to be obtained in a practically acceptable time.