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 ...

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 ...

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 evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...

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 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 ...

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 ...

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 ...

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 ...

In this chapter we will study the convex composite optimizations problem.