Given F : IR n ! IR m and a closed and convex set, the problem of nding x 2 IR n such that x 2 and F (x) = 0 is considered. For solving this problem an algorithm of Inexact-Newton type is de-ned. Global and local convergence proofs are presented. As a practical application, the Horizontal Nonlinear Complementarity Problem is introduced. It is shown that the Inexact-Newton algorithm can be appli...

Presented here is a generalization of the modified relative Newton method, recently proposed in [1] for quasi-maximum likelihood blind source separation. Special structure of the Hessian matrix allows to perform block-coordinate Newton descent, which significantly reduces the algorithm computational complexity and boosts its performance. Simulations based on artificial and real data show that t...

A new algorithm for rational interpolation is proposed. Given the data set, the algorithm generates a set of orthogonal polynomials by the classical threeterm recurrence relation and then uses Newton interpolation to find the numerator and the denominator polynomials of the rational interpolating function. The number of arithmetic operations of the algorithm to find a particular rational interp...

Abstract. In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as GaussNewton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution...

Presented here is a generalization of the relative Newton method, recently proposed for quasimaximum likelihood blind source separation. Special structure of the Hessian matrix allows performing block-coordinate Newton descent, which significantly reduces the algorithm computational complexity and boosts its performance. Simulations based on artificial and real data showed that the separation q...

To efficiently implement implicit Runge-Kutta (IRK) methods for solving large scale stiff ordinary differential equation systems, this paper proposes a new numerical algorithm, which contains a new modified Newton iterative method for solving the nonlinear stage equations of IRK, and two new rules for controlling the updating of Jacobian matrices. A convergence analysis shows that the new modif...

We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm of Lecerf, with now a polynomial complexity in the volume of the Newton polytope. We adopt a geometrical point of view, the main tool being derived from som...

We propose a fully distributed Newton-type algorithm for state estimation of electric power systems. At each Newton iteration, matrix-splitting techniques are utilized to carry out the matrix inversion for calculating the Newton step in a distributed fashion. In order to reduce the communication burden as well as increase robustness of state estimation, the proposed distributed scheme relies on...

This paper examines the e ectiveness of using a quasi-Newton based training of a feedforward neural network for forecasting. We have developed a novel quasi-Newton based training algorithm using a generalized logistic function. We have shown that a well designed feed forward structure can lead to a good forecast without the use of the more complicated feedback/feedforward structure of the recur...

The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...