Optimal Preconditioning for the Interval Parametric Gauss–Seidel Method
We deal with an interval parametric system of linear equations, and focus on the problem how to find an optimal preconditioning matrix for the interval parametric Gauss–Seidel method. The optimality criteria considered are to minimize the width of the resulting enclosure, to minimize its upper end-point or to maximize its lower end-point. We show that such optimal preconditioners can be computed by solving suitable linear programming problems. We also show by examples that, in some cases, such optimal preconditioners are able to significantly decrease an overestimation of the results of common methods.
KeywordsInterval computation Interval parametric system Preconditioner Linear programming
The author was supported by the Czech Science Foundation Grant P402-13-10660S.
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