zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A third-order Newton-type method to solve systems of nonlinear equations. (English) Zbl 1116.65060
Summary: We present a third-order Newton-type method to solve systems of nonlinear equations. In the first part we present theoretical preliminaries of the method. Secondly, we solve some systems of nonlinear equations. All test problems show the third-order convergence of our method.

65H10Systems of nonlinear equations (numerical methods)
Full Text: DOI
[1] Abbasbandy, S.: Improving Newton -- raphson method for nonlinear equations by modified Adomian decomposition method. Appl. math. Comput. 145, 887-893 (2003) · Zbl 1032.65048
[2] Chun, Ch.: A new iterative method for solving nonlinear equations. Appl. math. Comput. 178, No. 2, 415-422 (2006) · Zbl 1105.65057
[3] Chun, Ch.: Iterative methods improving Newton’s method by the decomposition method. Comput. math. Appl. 50, 1559-1568 (2005) · Zbl 1086.65048
[4] Frontini, M.; Sormani, E.: Third-order methods from quadrature formulae for solving systems of nonlinear equations. Appl. math. Comput. 149, 771-782 (2004) · Zbl 1050.65055
[5] Frontini, M.; Sormani, E.: Some variants of Newton’s method with third-order convergence. Appl. math. Comput. 140, 419-426 (2003) · Zbl 1037.65051
[6] Homeier, H. H. H.: On Newton-type methods with cubic convergence. J. comput. Appl. math. 176, 425-432 (2005) · Zbl 1063.65037