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)
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations. (English) Zbl 1123.65040
A class of globally convergent inexact Newton methods, the Newton-GMRES with quasi-conjugate-gradient backtracking (NGQCGB) methods, for solving large sparse systems of nonlinear equations are presented. These methods can be considered as a suitable combination of the Newton-GMRES iteration and some efficient backtracking strategies. In some cases, known Newton-GMRES backtracking (NGB) methods stagnate for some iterations or even fail. To avoid this disadvantage of NGB methods the authors propose a new alternative strategy, called quasi-conjugate-gradient with backtracking (QCGB), using the known information such as the projection of the gradient of the merit function on a proper subspace and last nonlinear step. Numerical computations show that the NGQCGB method is more robust and efficient than both the NGB method and the Newton-GMRES with eqality curve backtracking (NGECB) method.
MSC:
65H10Systems of nonlinear equations (numerical methods)
Software:
NITSOL