Nonlinear Systems of Equations

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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Ulrich Kulisch: Universität Karlsruhe, Institut für Angewandte Mathematik
Rolf Hammer: Universität Karlsruhe, Institut für Angewandte Mathematik
Matthias Hocks: Universität Karlsruhe, Institut für Angewandte Mathematik
Dietmar Ratz: Universität Karlsruhe, Institut für Angewandte Mathematik

Chapter Chapter 13 in C++ Toolbox for Verified Computing I, 1995, pp 293-311 from Springer

Abstract: 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.

Date: 1995
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DOI: 10.1007/978-3-642-79651-7_13

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