Abstract
The invariance of the topological degree under certain homotopies is used to derive a framework for tests to computationally prove the existence of zeros of nonlinear mappings in \({\mathbb {R}^{n}}\) . These tests use interval arithmetic to enclose the range of a function over a box and are provably more general than many other tests like the Moore–Kioustelidis test, a test based on the Krawczyk operator, and another degree–based test published recently. A numerical example is included.
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Beelitz, T., Frommer, A., Lang, B. et al. A framework for existence tests based on the topological degree and homotopy. Numer. Math. 111, 493–507 (2009). https://doi.org/10.1007/s00211-008-0193-3
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DOI: https://doi.org/10.1007/s00211-008-0193-3