Proving the existence of zeros using the topological degree and interval arithmetic
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Satisfiability of systems of equations of real analytic functions is quasi-decidable
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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We show how interval arithmetic can be used in connection with Borsuk's theorem to computationally prove the existence of a solution of a system of nonlinear equations. It turns out that this new test, which can be checked computationally in several different ways, is more general than an existing test based on Miranda's theorem in the sense that it is successful for a larger set of situations. A numerical example is included.