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Listar por autor "Argyros, Ioannis K"

Mostrando ítems 41-60 de 108

    • Generalized equations 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present some developments for the local convergence of Newton's method. Some special cases and a numerical example illuminating the theoretical results are also presented.

    • Generalized equations and newton’s and method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x)+Q(x) ϶ 0,(11.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ⟨., ...

    • Generalized newton method with applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      In this chapter we are interested in the approximately solving the generalized equation: Find x ∈ H such that 0 ∈ F(x) + T(x). (16.1) where F : H → H is a Fr→chet differentiable function, H is a Hilbert space and T : H ⇉ ...

    • Halley’s method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      In this chapter we are concerned with the problem of approximating a locally unique solution x* of the nonlinear equation F(x) = 0, where F is twice Fréchet-differentiable operator defined on a nonempty open and convex ...

    • Improved convergence analysis for Newton-like methods 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Numerical Algorithms, 04/2016)
      We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in ...

    • Improved local convergence analysis of the Gauss-Newton method under a majorant condition 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Computational Optimization and Applications, 03/2015)
      We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, 2008), ...

    • Improved semilocal convergence analysis in Banach space with applications to chemistry 

      Argyros, Ioannis K; Giménez de Ory, Elena ; Magreñán, Á. Alberto (Journal of Mathematical Chemistry, 2017)
      We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds ...

    • Improving the domain of parameters for Newton's method with applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto ; Sicilia, Juan Antonio (Journal of Computational and Applied Mathematics, 07/2017)
      We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...

    • Inexact gauss-newton method for least square problems 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      In this chapter we are interested in locating a solution x of the nonlinear least squares problem: minG(x) := 1/2 F(x)TF(x), (8.1) where F is Fréchet-differentiable defined on ℝn with values in ℝm, m ≥ n.

    • Inexact Newton Methods on Riemannian Manifolds 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Advances in iterative methods for nonlinear equations, 2016)
      In this chapter we study of the Inexact Newton Method in order to solve problems on a Riemannian Manifold. We present standard notation and previous results on Riemannian manifolds. A local convergence study is presented ...

    • Introduction to complex dynamics 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter some dynamical concepts of complex dynamics that will be used in this book are presented. Moreover, some graphics illustrating the theoretical concepts are shown in order to let the reader understand them better.

    • Iterative algorithms II 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Nova Science Publishers, 01/2016)
      The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with ...

    • Iterative methods and their dynamics with applications: A contemporary study 

      Argyros, Ioannis K; Magreñán, Á. Alberto (CRC Press, 2017)
      Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced ...

    • King-werner-like methods free of derivatives 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      Recently, Argyros and Ren in [6] studied King-Werner-like methods for approximating a locally unique solution x of equation (formula presented).

    • King-Werner-type methods of order 1 + √2 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-differentiable operator defined on a convex subset D of a Banach space X with ...

    • Laguerre-like method for multiple zeros 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter the applicability of the Laguerre-like method for finding multiple zeros is extended. Numerical examples are also presented.

    • Lavrentiev Regularization methods for Ill-posed equations 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      In this chapter, we consider the problem of approximately solving the nonlinear ill-posed operator equation of the form F(x) = y, (9.1) where F : D(F) ⊂ X → X is a monotone operator and X is a real Hilbert space. We denote ...

    • Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields 

      Argyros, Christopher I.; Argyros, Michael I; Argyros, Ioannis K; Magreñán, Á. Alberto; Sarría, Íñigo (Journal of Computational and Applied Mathematics, 2023)
      The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...

    • Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problems 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Applied Mathematics and Computation, 08/2014)
      We present a local convergence analysis of the proximal Gauss-Newton method for solving penalized nonlinear least squares problems in a Hilbert space setting. Using more precise majorant conditions than in earlier studies ...

    • Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation 

      Argyros, Ioannis K; Magreñán, Á. Alberto ; Orcos, Lara (Journal of Mathematical Chemistry, 08/2016)
      We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...