Nonlinear Systems of Equations Numerical Solution Halley’s and Euler-Chebyshev’s Methods Fixed-Point Relations
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 33, No 4, (2007), 433p-448p
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.