# Article

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Keywords:
numerical analysis
Summary:
In the paper there the effect of a substitution \$x_i=h_i(z_1,\ldots,z_n),\ i=1,\ldots,n\$ on the solution of a system of nonlinear equations \$f_i(x_1,\ldots, x_n)=0, i=1,\ldots, n\$ by the Newton-Raphson method is investigated. Formulas are derived which make possible the numerical calculation without actually performing the substitution. It is shown, that it is possible to derive formulas which keep the variables \$x_i\$ within certain bounds. All of them may be understood as the ordinary Newton-Raphson formula for the original system modified by a substitution.

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