ON OPTIMAL SOLUTION OF INTERVAL LINEAR EQUATIONS

摘要

For interval linear algebraic systems Ax = b, we consider the problem of componentwise evaluation of the set Sigma(There Exists There Exists)(A, b) = {A(-1)b parallel to A is an element of A, b is an element of 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 Sigma(There Exists There Exists) 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. [References: 33]