Bilateral approximations of solutions of equations by order three Steffensen-type methods
Abstract We study the convergence of a method of Steffensen-type, which is obtained from the Lagrange polynomial of inverse interpolation with…
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On approximating the inverse of a matrix
Abstract In this note we deal with two problems: the first regards the efficiency in approximating the inverse of a…
On the approximation of solutions to nonlinear operators between metric spaces
Abstract A Gauss-Seidel method for linear systems, based on decomposing the matrix system into four submatrices blocks, has been proposed…
A Halley-Aitken-type method for approximating the solutions of scalar equations
Abstract We are concerned with the approximation of the solution of scalar equations by Halley-Aitken method. We obtain local convergence…
On the convergence order of the multistep methods
Abstract We analyze in a unitary way the iterative methods for solving scalar equations, which are of inverse interpolation form.…
On the Chebyshev method for approximating the solutions of polynomial operator equations of degree 2
Abstract The Chebyshev method for approximating the solutions of polynomial operator equations of degree 2 is presented. The convergence of the Chebyshev…
Optimal efficiency indexes for iterative methods of interpolatory type
Abstract The paper is concerned with the order of convergence and the efficiency index of iterative methods of interpolatory type…
Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences
Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…
Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three
Abstract We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange…
On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations
Abstract It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled…