Abstract
The paper addresses the problem of solving linear algebraic systems the elements of which are, in the general case, nonlinear functions of a given set of independent parameters taking on their values within prescribed intervals. Three kinds of solutions are considered: (i) outer solution, (ii) interval hull solution, and (iii) inner solution. A simple direct method for computing a tight outer solution to such systems is suggested. It reduces, essentially, to inverting a real matrix and solving a system of real linear equations whose size n is the size of the original system. The interval hull solution (which is a NP-hard problem) can be easily determined if certain monotonicity conditions are fulfilled. The resulting method involves solving n+1 interval outer solution problems as well as 2n real linear systems of size n. A simple iterative method for computing an inner solution is also given. A numerical example illustrating the applicability of the methods suggested is solved.
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Kolev, L.V. Solving Linear Systems Whose Elements Are Nonlinear Functions of Intervals. Numerical Algorithms 37, 199–212 (2004). https://doi.org/10.1023/B:NUMA.0000049467.43979.94
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DOI: https://doi.org/10.1023/B:NUMA.0000049467.43979.94