Researchers introduced new concepts and arithmetic functions that could play a significant role in the quantum factorization problem. The Factorization Ensemble is the main one; it allows us to bind ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

The Helmholtz equation, a cornerstone in mathematical physics, models wave propagation phenomena in acoustics, electromagnetism and seismic imaging. Its inherent computational challenges—particularly ...

Rothe's method for parabolic initial boundary value problems, also known as the horizontal line method, consists of a time discretization by finite differences and leads to a sequence of boundary ...

This example solves a nonlinear system of equations by Newton's method. Let the nonlinear system be represented by ...

A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's ...