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

Kyurkchiev, Nikolay, and Iliev, Anton. "A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations." Serdica Mathematical Journal 33.4 (2007): 433-448. <http://eudml.org/doc/281433>.

@article{Kyurkchiev2007,
abstract = {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.},
author = {Kyurkchiev, Nikolay, Iliev, Anton},
journal = {Serdica Mathematical Journal},
keywords = {Nonlinear Systems of Equations; Numerical Solution; Halley’s and Euler-Chebyshev’s Methods; Fixed-Point Relations},
language = {eng},
number = {4},
pages = {433-448},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations},
url = {http://eudml.org/doc/281433},
volume = {33},
year = {2007},
}

TY - JOUR
AU - Kyurkchiev, Nikolay
AU - Iliev, Anton
TI - A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations
JO - Serdica Mathematical Journal
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 33
IS - 4
SP - 433
EP - 448
AB - 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.
LA - eng
KW - Nonlinear Systems of Equations; Numerical Solution; Halley’s and Euler-Chebyshev’s Methods; Fixed-Point Relations
UR - http://eudml.org/doc/281433
ER -