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    Iterative algorithms II 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Nova Science Publishers, 2016-01)
    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 ...

    Inexact Newton Methods on Riemannian Manifolds 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (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 ...

    Developments on the convergence of some iterative methods 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1); Sicilia, Juan Antonio (1) (Optimization and Dynamics with Their Applications: Essays in Honor of Ferenc Szidarovszky, 2017)
    Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of ...

    A contemporary study of iterative methods: Convergence, dynamics and applications 

    Magreñán, Á. Alberto (1); Argyros, Ioannis K (Elsevier, 2018)
    A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...

    Expanding kantorovich’s theorem for solving generalized equations 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (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, (22.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ...

    Iterative methods and their dynamics with applications: A contemporary study 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (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 ...

    Expanding the applicability of the gauss-newton method for convex optimization under restricted convergence domains and majorant conditions 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
    n this chapter we are concerned with the convex composite optimizations problem. This work is mainly motivated by the work in [17,23].We present a convergence analysis of Gauss-Newton method (defined by Algorithm (GNA) in ...

    Ball convergence for eighth order method 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
    Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a ...

    Directional newton methods and restricted domains 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
    Let F : D ⊂ ℝn → ℝ be a differentiable function. In computer graphics, we often need to compute and display the intersection C = A ⋂ B of two surfaces A and B in ℝ3 [5], [6]. If the two surfaces are explicitly given by A ...

    Gauss-newton method with applications to convex optimization 

    Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
    In this chapter we will study the convex composite optimizations problem.
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