2 research outputs found
On preconditioning and solving an extended class of interval parametric linear systems
We deal with interval parametric systems of linear equations and the goal is
to solve such systems, which basically comes down to finding an enclosure for a
parametric solution set. Obviously we want this enclosure to be as tight as
possible. The review of the available literature shows that in order to make a
system more tractable most of the solution methods use left preconditioning of
the system by the midpoint inverse. Surprisingly, and in contrast to standard
interval linear systems, our investigations have shown that double
preconditioning can be more efficient than a single one, both in terms of
checking the regularity of the system matrix and enclosing the solution set.
Consequently, right (which was hitherto mentioned in the context of checking
regularity of interval parametric matrices) and double preconditioning together
with the p-solution concept enable us to solve a larger class of interval
parametric linear systems than most of existing methods. The applicability of
the proposed approach to solving interval parametric linear systems is
illustrated by several numerical examples
Solution Sets of Complex Linear Interval Systems of Equations ∗
We present a solution set description for systems of complex interval equations, where complex intervals have a rectangular form. The solution set is described by a system of nonlinear inequalities, which can be used to obtain a very accurate approximation of the interval hull of the solution set. In our numerical experiments we exploit this approximation to study overestimation for common complex interval equation solvers (Gauss elimination, Hansen-Bliek-Rohn-Ning-Kearfott method)