Numerical solution to a system of nonlinear algebraic or transcendental equations with several parameters is constructed using the method of solution continuation with respect to the best parameter [1]. Necessary and sufficient conditions are proved for choosing the best parameters, which provide the best conditionality for system of linear equations of continuation. Such parameters have to be sought in the subspace tangent to the solution set of the system of nonlinear equations. This subspace is obtained if the original system of nonlinear equations is solved at the various parameter values from a given set. The parametric
approximation of curves and surfaces is considered.

[1]. V.I. Shalashilin, and E.B. Kuznetsov. Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics. Dordrecht / Boston / London: Kluwer Academic Publishers, (2003).