Related papers: Improved Aberth-Ehrlich root-finding algorithm and…
We present a convergence theory for Anderson acceleration (AA) applied to perturbed Newton methods (pNMs) for computing roots of nonlinear problems. Two important special cases are the classical Newton method and the Levenberg-Marquardt…
We introduced the package/subsystem GeoGebra Discovery to GeoGebra which supports the automated proving or discovering of elementary geometry inequalities. In this case study, for inequality exploration problems related to isosceles and…
In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem…
The attracting properties of gravity enable matter present in cores to collapse into stars with seven orders of magnitude change in space and time making modelling of star formation a challenging multi-scale process. To circumvent this…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
Koblitz curves are a special set of elliptic curves and have improved performance in computing scalar multiplication in elliptic curve cryptography due to the Frobenius endomorphism. Double-base number system approach for Frobenius…
We introduce a new method with spectral accuracy to solve linear non-autonomous ordinary differential equations (ODEs) of the kind $ \frac{d}{dt}\tilde{u}(t) = \tilde{f}(t) \tilde{u}(t)$, $\tilde{u}(-1)=1$, with $\tilde{f}(t)$ an analytic…
We implement a robust, globally convergent root search method for transcendental equations guaranteed to locate all complex roots within a specified search domain, based on Cauchy's residue theorem. Although several implementations of the…
We propose an approach to constructing iterative methods for finding polynomial roots simultaneously. One feature of this approach is using the fundamental theorem of symmetric polynomials. Within this framework, we reconstruct many of the…
Realizing high-throughput aberration-corrected Scanning Transmission Electron Microscopy (STEM) exploration of atomic structures requires rapid tuning of multipole probe correctors while compensating for the inevitable drift of the optical…
Univariate polynomial root-finding has been studied for four millennia and very intensively in the last decades. Our new near-optimal root-finders approximate all zeros of a polynomial p almost as fast as one accesses its coefficients with…
The problem of gravitational wave parameter estimation and source localization is crucial in gravitational wave astronomy. Gravitational waves emitted by compact binary coalescences in the sensitivity band of second-generation ground-based…
The detection rate for compact binary mergers has grown as the sensitivity of the global network of ground based gravitational wave detectors has improved, now reaching the stage where robust automation of the analyses is essential.…
In this paper, we study functions of the roots of a univariate polynomial in which the roots have a given multiplicity structure $\mu$. Traditionally, root functions are studied via the theory of symmetric polynomials; we extend this theory…
The mergers of neutron star-neutron star and neutron star-black hole binaries are the most promising gravitational wave events with electromagnetic counterparts. The rapid detection, localization and simultaneous multi-messenger follow-up…
The aim of this paper is the study of the bisection method in $\mathbb{R}^n$. In this work we propose a multivariate bisection method supported by the Poincar\'e-Miranda theorem in order to solve non-linear system of equations. Given an…
For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an…
A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…
Ground-based solar image restoration is a computationally expensive procedure that involves nonlinear optimization techniques. The presence of atmospheric turbulence produces perturbations in individual images that make it necessary to…
In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are called root-finding problems. Our first algorithm is…