Geometric constructions of iterative functions to solve nonlinear equations

Amat, Sergio; Busquier, Sonia; Jiménez, José Manuel Gutiérrez

doi:10.1016/s0377-0427(03)00420-5

Cited by 261 publications

(145 citation statements)

References 14 publications

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“…This family includes the classical Chebyshevs method (CM), (α = 0) , Halleys method (HM) (α = 1/2) and Super-Halley method (SHM) (α = 1)) (for the details of these methods, see [17][18] or a recent review [19]). In order to improve the local order of convergence, Grau and Daz-Barrero [20] propose an improvement of Chebyshevs method with fifth-order convergencẽ…”

Section: Nonlinear Equations Based On Newtons Methodsmentioning

confidence: 99%

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The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

Nouri

Safarinia²,

Pourmahdi³

et al. 2014

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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In this paper a parallel Hash algorithm construction based on the Chebyshev Halley methods with variable parameters is proposed and analyzed. The two core characteristics of the recommended algorithm are parallel processing mode and chaotic behaviors. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. The proposed algorithm contains variable parameters dynamically obtained from the position index of the corresponding message blocks. Theoretical analysis and computer simulation indicate that the algorithm can assure all performance requirements of hash function in an efficient and flexible style and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

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Section: Nonlinear Equations Based On Newtons Methodsmentioning

confidence: 99%

“…Shannon introduced diffusion and confusion in order to hide message redundancy [18,19]. Hash function, like encryption system, requires the plaintext to diffuse its influence into the whole Hash space.…”

Section: Statistical Analysis Of Diffusion and Confusionmentioning

confidence: 99%

The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

Nouri

Safarinia²,

Pourmahdi³

et al. 2014

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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show abstract

“…. , (1.6) where x 0 ∈ D is an initial point and F (x n ) † denotes the Moore-Penrose inverse of the linear operator (of matrix) F (x n ) [1,12,14,15,17,18,20,21,36].…”

Section: Introductionmentioning

confidence: 99%

Extended local convergence analysis of inexact Gauss-Newton method for singular systems of equations under weak conditions

Argyros

George

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract.A new local convergence analysis of the Gauss-Newton method for solving some optimization problems is presented using restricted convergence domains. The results extend the applicability of the Gauss-Newton method under the same computational cost given in earlier studies. In particular, the advantages are: the error estimates on the distances involved are tighter and the convergence ball is at least as large. Moreover, the majorant function in contrast to earlier studies is not necessarily differentiable. Numerical examples are also provided in this study.Mathematics Subject Classification (2010): 65D10, 65D99, 65G99, 65K10, 90C30.

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“…A plethora of sufficient conditions for the local as well as the semilocal convergence of Newton-type methods as well as an error analysis for such methods can be found in [1]- [22].…”

Section: Introductionmentioning

confidence: 99%

Local Convergence of the Gauss-Newton Method for Injective-Overdetermined Systems

Amat¹,

Argyros²,

Magreñán³

2014

Journal of the Korean Mathematical Society

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Abstract. We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10,11,13,14,18]. Special cases and numerical examples are also included in this study.

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Geometric constructions of iterative functions to solve nonlinear equations

Cited by 261 publications

References 14 publications

The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

Extended local convergence analysis of inexact Gauss-Newton method for singular systems of equations under weak conditions

Local Convergence of the Gauss-Newton Method for Injective-Overdetermined Systems

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