Related papers: Modified Potra-Pt\'ak method to determine the mult…
Computing the matrix square root or its inverse in a differentiable manner is important in a variety of computer vision tasks. Previous methods either adopt the Singular Value Decomposition (SVD) to explicitly factorize the matrix or use…
We investigate Newton's method as a root finder for complex polynomials of arbitrary degree. While polynomial root finding continues to be one of the fundamental tasks of computing, with essential use in all areas of theoretical…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
The aim of this paper is to introduce a new Newton-type iterative method and then to show that this process converges to the unique solution of the scalar nonlinear equation f(x)=0 under weaker conditions involving only f and f' by fixed…
Iterative methods for nonlinear monotone equations do not require the differentiability assumption on the residual function. This special property of the methods makes them suitable for solving large-scale nonsmooth monotone equations. In…
Acceleration is an increasingly common theme in the stochastic optimization literature. The two most common examples are Nesterov's method, and Polyak's momentum technique. In this paper two new algorithms are introduced for root finding…
Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix $p$th root, and its computational cost is $\mathcal{O}(n^3p)$ flops per iteration. In this paper, a cost-efficient variant of IN iteration is…
We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
We introduce a new iterative root-finding method for complex polynomials, dubbed {\it Newton-Ellipsoid} method. It is inspired by the Ellipsoid method, a classical method in optimization, and a property of Newton's Method derived in…
In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining…
Given the $n\times n$ matrix polynomial $P(x)=\sum_{i=0}^kP_i x^i$, we consider the associated polynomial eigenvalue problem. This problem, viewed in terms of computing the roots of the scalar polynomial $\det P(x)$, is treated in…
In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…
We construct a family of iterations for computing the principal square root of a square matrix $A$ using Zolotarev's rational minimax approximants of the square root function. We show that these rational functions obey a recursion, allowing…
In the present study, a numerical method, perturbation-iteration algorithm (shortly PIA), have been employed to give approximate solutions of nonlinear fractional-integro differential equations (FIDEs). Comparing with the exact solution,…
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Those spaces are then endowed with the Gaussian probability…
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
In this note, we present an eighth-order derivative-free family of iterative methods for nonlinear equations. The proposed family shows optimal eight-order of convergence in the sense of the Kung and Traub conjecture \cite{5} and is based…