Related papers: A Newton method for harmonic mappings in the plane
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Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
Harmonic polylogarithms $\H(\vec{a};x)$, a generalization of Nielsen's polylogarithms ${S}_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical…
A new version of the Graeffe algorithm for finding all the roots of univariate complex polynomials is proposed. It is obtained from the classical algorithm by a process analogous to renormalization of dynamical systems. This iteration is…
The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…
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An iterative map of the unit disc in the complex plane (Appendix) is used to explore certain aspects of selfdual, four dimensional gauge fields (quasi)periodic in the Euclidean time. These fields are characterized by two topological numbers…
Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
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The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
The Newton map N_f of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of N_f. We study the behavior of N_f in a component V of C\U. If V can be…
Given a polynomial system f associated with a simple multiple zero x of multiplicity {\mu}, we give a computable lower bound on the minimal distance between the simple multiple zero x and other zeros of f. If x is only given with limited…
In this paper we numerically explore the convergence properties of the pseudo-Newtonian circular restricted problem of three and four primary bodies. The classical Newton-Raphson iterative scheme is used for revealing the basins of…
We show, that the Complex Step approximation to the Fr\'echet derivative of real matrix functions is applicable to the matrix sign, square root and polar mapping using iterative schemes. While this property was already discovered for the…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…