majorizing sequences
advantages
convergence analysis
On the complexity of choosing majorizing sequences for iterative procedures
cases
article
Banach
literature
criteria
multi-point procedures
constants
Newton-type
applications
complexity
Aitken
Stirling
Newton
en
idea
special case
Lipschitz constants
false
convergence
numerous procedures
old constants
equations
hypothesis
local convergence
sequence
aforementioned procedures
multi-step multi-point procedures
2022-01-01T18:49
Picard
iterative procedure
secant
study
additional hypotheses
convergence criteria
2018-06-30
Steffensen
nonlinear equations
The aim of this paper is to introduce general majorizing sequences for iterative procedures which may contain a non-differentiable operator in order to solve nonlinear equations involving Banach valued operators. A general semi-local convergence analysis is presented based on majorizing sequences. The convergence criteria, if specialized can be used to study the convergence of numerous procedures such as Picard’s, Newton’s, Newton-type, Stirling’s, Secant, Secant-type, Steffensen’s, Aitken’s, Kurchatov’s and other procedures. The convergence criteria are flexible enough, so if specialized are weaker than the criteria given by the aforementioned procedures. Moreover, the convergence analysis is at least as tight. Furthermore, these advantages are obtained using Lipschitz constants that are least as tight as the ones already used in the literature. Consequently, no additional hypotheses are needed, since the new constants are special cases of the old constants. These ideas can be used to study, the local convergence, multi-step multi-point procedures along the same lines. Some applications are also provided in this study.
lines
analysis
aim
non-differentiable operators
Kurchatov
one
operators
new constants
semi-local convergence analysis
2018-06-30
paper
articles
Secant-type
order
general semi-local convergence analysis
1463-1473
procedure
https://doi.org/10.1007/s13398-018-0561-5
https://scigraph.springernature.com/explorer/license/
same line
Argyros
Ioannis K.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Springer Nature
1578-7303
1579-1505
Pure Mathematics
113
Santhosh
George
pub.1105223602
dimensions_id
Department of Mathematical Sciences, Cameron University, 73505, Lawton, OK, USA
Department of Mathematical Sciences, Cameron University, 73505, Lawton, OK, USA
Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, Mangalore, India
Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, Mangalore, India
Mathematical Sciences
Springer Nature - SN SciGraph project
10.1007/s13398-018-0561-5
doi
2