Numerical solution of nonlinear equations by one-parameter imbedding methods

The aim of the paper is a systematic study of one-parameter imbedding methods applied to systems of nonlinear algebraic equations. The algorithms considered are classified as one-loop and multi-loop, respectively. The paper presents several multi-loop algorithms designed for solving equations in a general operator form. Some sufficient conditions for the construction of suitable algorithms with respect to the convergence are given in the paper for the case of algebraic systems, including a detailed discussion of some relations between one-step iterative and imbedding methods. The effectiveness of various imbedding algorithms is tested on a set of problems. It is shown that some of the imbedding methods can be good alternative othe classical Newton's method whilst the majority of methods considered did not give an improvement of the rate of convergence. An advantage of the imbedding methods may be their possib le broadening of the domain of attraction of some solutions.