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)
Local convergence of inexact methods under the Hölder condition. (English) Zbl 1181.65082
The convergence properties are studied for some inexact Newton-like methods for solving nonlinear operator equations in Banach spaces. In practice the Newton method has two disadvantages: it requires computing exactly Jacobian matrices and secondly, it requires solving exactly the corresponding linear equations. In this paper such inexact Newton-like methods avoiding both disadvantages are developed using a new type of residual control. Under the assumption that the derivative of the operator defining the equation satisfies the Hölder condition, the radius of the convergence ball of the inexact Newton-like methods with the new type residual control is estimated, and a linear and superlinear convergence rate is proved. A slight modification of the inexact Newton-like method of R. H. Chan, H. L. Chang and S. F. Xu [BIT 43, No. 1, 7–20 (2003; Zbl 1029.65036)] for solving inverse eigenvalue problems is proposed. A numerical example for illustrating the performance of the latter algorithm is presented.
MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)