Related papers: Annealing approach to root-finding
Newton-Raphson method in complex space is used to numerically solve the transcendental dispersion relation of low frequency shear Alfven waves in fusion plasmas. The equation exhibits several physically relevant basins of attraction. The…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the…
The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to search roots inside a pre-specified region…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial. They can be approximated at a low computational cost if the…
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…
A method is given for finding roots of a one-variable function using Taylor's expansion of that function and fractional derivative calculated at a suitable tangent point without using Newton's method, but is regarded as a variant of Halley…
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We…
In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the…
The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical…
We depart from our approximation of 2000 of all root radii of a polynomial, which has readily extended Sch{\"o}nhage's efficient algorithm of 1982 for a single root radius. We revisit this extension, advance it, based on our simple but…
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author.…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
This paper is triggered by the preprint "\emph{Computing Matrix Squareroot via Non Convex Local Search}" by Jain et al. (\textit{\textcolor{blue}{arXiv:1507.05854}}), which analyzes gradient-descent for computing the square root of a…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…