Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 lor end-point.  show that such optimal preconditioners can be computed by solving suitable linear programming problems.  also show by examples that, in some cases, such optimal preconditioners are able to significantly decrease an overestimation of the results of common methods.
['Milan Hladík']
I am writing a research paper on a idea Optimal Preconditioning for the Interval Parametric Gauss---Seidel Method
[{"from": "human", "value": "I am writing a research paper on a idea Optimal Preconditioning for the Interval Parametric Gauss---Seidel Method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 lor end-point.  show that such optimal preconditioners can be computed by solving suitable linear programming problems.  also show by examples that, in some cases, such optimal preconditioners are able to significantly decrease an overestimation of the results of common methods."}]