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

Kyurkchiev, Nikolay; Iliev, Anton

Serdica Mathematical Journal (2007)

- Volume: 33, Issue: 4, page 433-448
- ISSN: 1310-6600

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topKyurkchiev, 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 -

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