In this chapter we are concerned with approximating a solution of the equation f(x) = 0, (15.1) where f is defined on an open domain or closed domain D on a real space ℝ.

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 ...

We study the variational inclusion 0 ∈ F(x) + G(x) + E(x), (17.1) where X, Y are Banach space D ⊂ X is an open set F : D → Y is a smooth operator, G : D → Y is continuous operator, [., .;G] is a divided difference of order ...

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 ...

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 ⟨., ...

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 ...

In this work, we are concerned with the problem of developing a general theory about derivative-free iterative procedures with quadratic convergence. Newton's method is the most used, well-known and studied in order to ...

The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning ...

Let S = ℝ or S = ℂ, D ⊆ S be convex and let F : D → S be a differentiable function. We shall approximate solutions x of the equation F(x) = 0, (5.1) Many problems from Applied Sciences including engineering can be solved ...

We determine a solution x of the equation F(x) = 0. where X and Y are Banach spaces, D ⊆ X a convex set and F : D → Y is a Fréchet-differentiable operator. In particular, we expand the applicability of the Newton’s method ...