On Optimal Solution of Interval Linear Equations
Sergey P. Shary · SIAM Journal on Numerical Analysis · 1995
For interval linear algebraic systems ${\bf A}x = {\bf b}$, we consider the problem of component-wise evaluation of the set $\Sigma _{\exists \exists } ({\bf A},{\bf b}) = \{ {A^{ - 1} b\mid A \in {\bf A},b \in {\bf b}} \}$ formed by all solutions of $Ax = b$ when A and b vary independently in ${\bf A}$ and ${\bf b}$, respectively. An iterative PSS algorithm is introduced that computes optimal (exact) componentwise estimates of $\Sigma _{\exists \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.