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 new third-order family of nonlinear solvers for multiple roots. (English) Zbl 1198.65089
Summary: In this paper, a new family of third-order methods for finding multiple roots of nonlinear equations has been introduced. This family requires one-function and two-derivative evaluation per iteration. The family contains several known third-order methods, as special cases. Some examples are presented to show the performance of the presented family.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Traub, J. F.: Iterative methods for the solution of equations, (1964) · Zbl 0121.11204
[2] Hansen, E.; Patrick, M.: A family of root finding methods, Numer. math. 27, 257-269 (1977) · Zbl 0361.65041 · doi:10.1007/BF01396176
[3] Victory, H. D.; Neta, B.: A higher order method for multiple zeros of nonlinear functions, Int. J. Comput. math. 12, 329-335 (1983) · Zbl 0499.65026 · doi:10.1080/00207168208803346
[4] Dong, C. C.: A family of multipoint iterative functions for finding multiple roots, Int. J. Comput. math. 21, 363-367 (1987) · Zbl 0656.65050 · doi:10.1080/00207168708803576
[5] Neta, B.; Johnson, A. N.: High order nonlinear solver for multiple roots, Comput. math. Appl. 55, 2012-2017 (2008) · Zbl 1142.65044 · doi:10.1016/j.camwa.2007.09.001
[6] Osada, N.: An optimal multiple root-finding method of order three, J. comput. Appl. math. 51, 131-133 (1994) · Zbl 0814.65045 · doi:10.1016/0377-0427(94)00044-1
[7] Chun, C.; Neta, B.: A third-order modification of Newton’s method for multiple roots, Appl. math. Comput. 211, 474-479 (2009) · Zbl 1162.65342 · doi:10.1016/j.amc.2009.01.087
[8] Chun, C.; Bae, H. J.; Neta, B.: New families of nonlinear third-order solvers for finding multiple roots, Comput. math. Appl. 57, 1574-1582 (2009) · Zbl 1186.65060 · doi:10.1016/j.camwa.2008.10.070
[9] Gautschi, W.: Numerical analysis: an introduction, (1997) · Zbl 0877.65001