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)
An optimal multiple root-finding method of order three. (English) Zbl 0814.65045
An optimal one-point iterative method of order three for determining a multiple zero of a complex function in a complex variable which requires less computational effort per iteration step than three known such optimal methods is presented. One numerical example with a non-real zero of multiplicity 5/2 is given.

65H05Single nonlinear equations (numerical methods)
65E05Numerical methods in complex analysis
30C15Zeros of polynomials, etc. (one complex variable)
Full Text: DOI
[1] Hansen, T.; Patrick, M.: A family of root finding methods. Numer. math. 27, 257-269 (1977) · Zbl 0361.65041
[2] Ostrowski, A. M.: Solution of equations in Euclidean and Banach spaces. (1973) · Zbl 0304.65002
[3] Traub, J. F.: Iterative methods for the solution of equations. (1982) · Zbl 0472.65040