Continuation of solutions in multiparameter approximation of curves and surfaces

When a system of nonlinear algebraic or transcendental equations with several parameters is solved numerically, the best parameters within the framework of the continuation method have to be sought in the tangent space of the solution set of this system. More specifically, these parameters have to be sought in the directions of the eigenvectors of a linear self-adjoint transformation. Algorithms for the best parametrization of curves and surfaces are proposed. Numerical examples of parametric interpolation of surfaces confirm previously known theoretical results.