In this paper, a set of Root mean square derivative based closed Newton Cotes quadrature formula (RMSDCNC) is introduced in which the derivative value is included in addition to the existing closed Newton Cotes quadrature (CNC) formula for the calculation of a definite integral in the inetrval [a, b]. These derivative value is measured by using the root mean square value. The proposed formula y...

An iterative formula based on Newton’s method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional NewtonMethodmay fail to converge to the desired root. In addition, themethod has super-quadratic convergence of order 2.414 (i.e., 1 + √2). Newton method is said to fail in certain cases leading to oscillation, divergence to increasing...

Matrix fixed-point iterations zn+1 = ψ(zn) defined by a rational function ψ are considered. For these iterations a new proof is given that matrix convergence is essentially reduced to scalar convergence. It is shown that the principal Padé family of iterations for the matrix sign function and the matrix square root is a special case of a family of rational iterations due to Ernst Schröder. This...

the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

A Ulm-like method is proposed in [13] for solving inverse eigenvalue problems with distinct given eigenvalues. The Ulm-like method avoids solving the Jacobian equations used in Newton-like methods and is shown to be quadratically convergent in the root sense. However, the numerical experiments in [3] only show that the Ulm-like method is comparable to the inexact Newton-like method. In this sho...

Abstract. We present a method for solving systems of nonlinear equations suitable for problems where convergence of an approximate Newton method is initially slow. The method, nonlinear elimination (NIEm), eliminates the nonlinear equations and appropriate variables deemed to be causing the problem. An analysis of the method is given and leads to a detailed algorithm that reduces automatically ...

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...