Abstract
In Chapter 6, we considered the problem of finding zeros (or roots) of nonlinear functions of a single variable. Now, we consider its generalization, the problem of finding the solution vectors of a system of nonlinear equations. We give a method for finding all solutions of a nonlinear system of equations f(x) = 0 for a continuously differentiable function f: ℝn→ ℝn in a given interval vector (box). Our method computes close bounds on the solution vectors, and it delivers information about existence and uniqueness of the computed solutions. The method we present is a variant of the interval Gauss-Seidel method based on the method of Hansen and Sengupta [3], [32], and a modification of Ratz [79]. Our method makes use of the extended interval operations defined in Section 3.3.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kulisch, U., Hammer, R., Hocks, M., Ratz, D. (1995). Nonlinear Systems of Equations. In: C++ Toolbox for Verified Computing I. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79651-7_13
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DOI: https://doi.org/10.1007/978-3-642-79651-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-79653-1
Online ISBN: 978-3-642-79651-7
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