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Solving \(N+m\) nonlinear equations with only m nonlinear variables. (English) Zbl 0721.65024
We derive a method for solving \(N+m\) nonlinear algebraic equations in \(N+m\) unknowns \(y\in {\mathbb{R}}^ m\) and \(z\in {\mathbb{R}}^ N\) of the form \(A(y)z+b(y)=0\), where the \((N+m)\times N\) matrix A(y) and vector b(y) are continuously differentiable functions of y alone. By exploiting properties of an orthonormal basis for \(null(A^ T(y))\) the problem is reduced to solving m nonlinear equations in y only. These equations are solved by Newton’s method in m variables. Details of computational implementation and results are provided.
Reviewer: T.J.Ypma

MSC:
65H10 Numerical computation of solutions to systems of equations
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