Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 27

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
1
Content available remote

On an iterative method for unconstrained optimization

100%
Argyros I.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 4
333-342
EN
We present a local and a semi-local convergence analysis of an iterative method for approximating zeros of derivatives for solving univariate and unconstrained optimization problems. In the local case, the radius of convergence is obtained, whereas in the semi-local case, sufficient convergence criteria are presented. Numerical examples are also provided.
2
Content available remote

A convergence analysis of Newton's method under the gamma-condition in Banach spaces

100%
Argyros I.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 2
225-239
EN
We provide a local as well as a semilocal convergence analysis for Newton's method to approximate a locally unique solution of an equation in a Banach space setting. Using a combination of center-gamma with a gamma-condition, we obtain an upper bound on the inverses of the operators involved which can be more precise than those given in the elegant works by Smale, Wang, and Zhao and Wang. This observation leads (under the same or less computational cost) to a convergence analysis with the following advantages: local case: larger radius of convergence and finer error estimates on the distances involved; semilocal case: larger domain of convergence, finer error bounds on the distances involved, and at least as precise information on the location of the solution.
3
Content available remote

On the Newton-Kantorovich theorem and nonlinear finite element methods

100%
Argyros I.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 1
75-81
EN
Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
4
Content available remote

On the gap between the semilocal convergence domains of two Newton methods

100%
Argyros I.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 2
193-204
EN
We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at least as precise information on the location of the solution; and a smaller gap between the two methods.
5
Content available remote

A weaker affine covariant Newton-Mysovskikh theorem for solving equations

100%
Argyros I.
Applicationes Mathematicae
|
2006
|
tom 33
|
nr 3-4
355-363
EN
The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.
6
Content available remote

A new approach for finding weaker conditions for the convergence of Newton's method

100%
Argyros I.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 4
465-475
EN
The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the solution can be obtained this way. Here we show that we can further weaken conditions (18)-(20) and still improve on the error bounds given in [3], [4] (see Remark 1(c)).
7
Content available remote

A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses

100%
Argyros I.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 1
37-49
EN
The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich hypothesis is violated.
8
Content available remote

On the convergence and application of Stirling's method

100%
Argyros I.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 1
109-119
EN
We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
9
Content available remote

On the solution and applications of generalized equations using Newton's method

100%
Argyros I.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 2
229-242
EN
We provide local and semilocal convergence results for Newton's method when used to solve generalized equations. Using Lipschitz as well as center-Lipschitz conditions on the operators involved instead of just Lipschitz conditions we show that our Newton-Kantorovich hypotheses are weaker than earlier sufficient conditions for the convergence of Newton's method. In the semilocal case we provide finer error bounds and a better information on the location of the solution. In the local case we can provide a larger convergence radius. Our results apply to generalized equations involving single as well as multivalued operators, which include variational inequalities, nonlinear complementarity problems and nonsmooth convex minimization problems.
10
Content available remote

New unifying convergence criteria for Newton-like methods

100%
Argyros I.
Applicationes Mathematicae
|
2002
|
tom 29
|
nr 3
359-369
EN
We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius.
11
Content available remote

On a new method for enlarging the radius of convergence for Newton's method

100%
Argyros I.
Applicationes Mathematicae
|
2001
|
tom 28
|
nr 1
1-15
EN
We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
12
Content available remote

Local convergence theorems for Newton's method from data at one point

100%
Argyros I.
Applicationes Mathematicae
|
2002
|
tom 29
|
nr 4
481-486
EN
We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
13
Content available remote

Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions

64%
Argyros I., George S.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 2-3
193-203
EN
We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
14
Content available remote

Local convergence of two competing third order methods in Banach space

64%
Argyros I., George S.
Applicationes Mathematicae
|
2014
|
tom 41
|
nr 4
341-350
EN
We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.
15
Content available remote

An improved convergence analysis of Newton's method for twice Fréchet differentiable operators

64%
Argyros I., Khattri S.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 4
459-481
EN
We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.
16
Content available remote

On the Halley method in Banach spaces

64%
Argyros I., Ren H.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 2
243-255
EN
We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.
17
Content available remote

Improved ball convergence of Newton's method under general conditions

64%
Argyros I., Ren H.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 3
365-375
EN
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.
18
Content available remote

Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions

64%
Argyros I., Hilout S.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 2
193-209
EN
We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
19
Content available remote

On the convergence of Newton's method under ω*-conditioned second derivative

64%
Argyros I., Hilout S.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 3
341-355
EN
We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
20
Content available remote

Expanding the applicability of two-point Newton-like methods under generalized conditions

64%
Argyros I., Hilout S.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 1
63-90
EN
We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.