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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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##### References:
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