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2002

On Existence and Uniqueness Verification for Non-Smooth Functions

9 years 3 months ago
On Existence and Uniqueness Verification for Non-Smooth Functions
Given an approximate solution to a nonlinear system of equations at which the Jacobi matrix is nonsingular, and given that the Jacobi matrix is continuous in a region about this approximate solution, a small box can be constructed about the approximate solution in which interval Newton methods can verify existence and uniqueness of an actual solution. Recently, we have shown how to verify existence and uniqueness, up to multiplicity, for solutions at which the Jacobi matrix is singular. We do this by efficient computation of the topological index over a small box containing the approximate solution. Since the topological index is defined and computable when the Jacobi matrix is not even defined at the solution, one may speculate that efficient algorithms can be devised for verification in this case, too. In this note, however, we discuss, through examples, key techniques in underlying our simplification of the calculations that cannot necessarily be used when the function is non-smooth...
R. Baker Kearfott
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 2002
Where RC
Authors R. Baker Kearfott
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