Multidimensional Parametrization and NumericalSolution of Systems of Nonlinear Equations

摘要

The numerical solution of a system of nonlinear algebraic or transcendental equations isexamined within the framework of the parameter continuation method. An earlier result of the authoraccording to which the best parameters should be sought in the tangent space of the solution set of thissystem is now refined to show that the directions of the eigenvectors of a certain linear self-adjointoperator should be used for finding these parameters. These directions correspond to the extremal val-ues of the quadratic form associated with the above operator. The parametric approximation of curvesand surfaces is considered.