Noise plays a uniquely informative role in connection with the particle-wave duality. It was Albert Einstein who first realized (in 1909) that electromagnetic fluctuations are different if the energy is carried by waves or by particles. The magnitude of energy fluctuations scales linearly with the mean energy for classical waves, but it scales with the square root of the mean energy for classic...

A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the “α + n conjecture” and the “nα conjecture”. These say, respectively, that given any algebraic integer α there is a natural number n such ...

Let φ(x) be an Eisenstein polynomial of degree n over a local field and α be a root of φ(x). Our main tool is the ramification polygon of φ(x), that is the Newton polygon of ρ(x) = φ(αx+α)/(αx). We present a method for determining the Galois group of φ(x) in the case where the ramification polygon consists of one segment.

In this paper we discuss a parallel variant of the interval Newton method for root finding of non linear continuously differentiable functions on the CUDA architecture. For this purpose we have investigated different dynamic load balancing methods to get an evenly balanced workload during the parallel computation. We tested the functionality, correctness and performance of our implementation in...

Among many existing algorithms, convergence methods are the most popular means of computing square root and the reciprocal of square root of numbers. An initial approximation is required in these methods. Look up tables (LUT) are employed to produce the initial approximation. In this paper a number of methods are suggested to reduce the size of the look up tables. The precision of the initial a...

Square root plays a major role in applications like computer graphics, image processing. To increase the performance of computation, many algorithms have been proposed to carry out the computation task in hardware instead of software. One very common and relatively quick method for finding the square root of a number is the Newton-Raphson method which requires extensive use of division to produ...

In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

In this paper, a Ulm-like method is proposed for solving inverse singular value problems. This method has an advantage over Newton’s methods since it avoids solving approximate Jacobian equations. Under some mild assumptions, we show that the proposed method converges at least quadratically in the root sense. Our numerical tests, based on comparison with the inexact Newton method given by Bai a...

Abstract. Various writers have dealt with the subject of optimal starting approximations for square-root calculation by Newton's method. Three optimality criteria that have been used can be shown to lead to closely related approximations. This fact makes it surprisingly easy to choose a starting approximation of some prescribed form so that the maximum relative error after any number of Newton ...