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A numerical approach to \(2k+e\) nonlinear equations with only \(k\) nonlinear variables. (English) Zbl 0754.65045
The author derives a method for solving \(2k+e\) nonlinear algebraic equations in \(2k\) unknowns of the form \(L(x)y-b=0\) with unknowns \(x\) and \(y\), where \(e\) is a positive integer and the entries of the \((2k+e)\times k\) matrix \(L(x)\) are nonlinear functions of \(x\). The method is based on solving a linear overdetermined system and a polynomial equation of the \(k\)-th order. Some numerical tests are also presented.

MSC:
65H10 Numerical computation of solutions to systems of equations
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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