zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
New iterative schemes for nonlinear equations. (English) Zbl 1116.65056
Summary: We suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method. We also discuss the convergence criteria of these iterative methods. Several numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations.

MSC:
65H05Single nonlinear equations (numerical methods)
WorldCat.org
Full Text: DOI
References:
[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] Adomian, G.: Nonlinear stochastic systems and applications to physics. (1989) · Zbl 0659.93003
[3] Chun, C.: Iterative methods improving Newton’s method by the decomposition method. Comput. math. Appl. 50, 1559-1568 (2005) · Zbl 1086.65048
[4] He, J. H.: A new iterative method for solving algebraic equations. Appl. math. Comput. 135, 81-84 (2005)
[5] Homeier, H. H.: On Newton-type methods with cubic convergence. J. comput. Appl. math. 176, 425-432 (2005) · Zbl 1063.65037
[6] M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2006.
[7] M. Aslam Noor, K. Inayat Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.05.084.
[8] Luo, X.: A note on the new iteration for solving algebraic equations. Appl. math. Comput. 171, 1177-1183 (2005) · Zbl 1091.65044