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Title: A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations
Authors: Kyurkchiev, Nikolay
Iliev, Anton
Keywords: Nonlinear Systems of Equations
Numerical Solution
Halley’s and Euler-Chebyshev’s Methods
Fixed-Point Relations
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 33, No 4, (2007), 433p-448p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 65H10.
ISSN: 1310-6600
Appears in Collections:Volume 33, Number 4

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