This leads to a topological criterion for the existence of bifurcations in iterative root-finding algorithms based on rational maps (such as Newton’s method). For example, any such algorithm must fail on every neighborhood of p(X) = Xd when d is 4 or more. We show that on such neighborhoods one cannot even continuously assign to each polynomial p an expanding rational map Tp such that the attra...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

This paper presents a new algorithm to find non-zero real root of the non-linear transcendental equations. The proposed method is based on combination inverse sine series and Newton-Raphson method. Implementation in MATLAB applied different problems ensure methods applicability. Error calculation has been done for available existing suggested evaluated using number numerical examples results in...

Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

We show that a plane algebraic curve f = 0 over the complex numbers has on it either at most 22V (f) points whose coordinates are both roots of unity, or infinitely many such points. Here V (f) is the area of the Newton polytope of f. We present an algorithm for finding all these points.

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

The use of matching pursuits (MP) to compress motion compensated residual video signals and its extension to layered coding have recently been demonstrated in [1, 2]. In this paper we describe a multi-pass rate control scheme for SNR scalable encoding based on MP. The rate control algorithm enforces constant quality on each layer, while keeping the bit budget for each layer at a pre-specified t...