A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Here we give methodological survey of contemporary methods for solving nonlinear systems of equations in Rn. The reason of this review is that many authors in present days rediscovered such classical methods. In particular, we consider Newton’s-type algorithms with sparse Jacobian. Method for which the inverse matrix of the Jacobian is replaced by the inverse matrix of the Vandermondian is proposed. A number of illustrative numerical examples are displayed. We demonstrate Herzberger’s model with fixed-point relations to the some discrete versions of Halley’s and Euler-Chebyshev’s methods for solving such kind of systems.