68 citations · 169 across the 22 of their papers we have counts for
5 papers · 1 filter
On the iterative solution of systems of the form
Henri Calandra, Serge Gratton, Elisa Riccietti +1
Given a full column rank matrix (), we consider a special class of linear systems of the form with $x, c \in \mathbb{…
Exploiting variable precision in GMRES
Serge Gratton, Ehouarn Simon, David Titley-Peloquin +1
We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm…
On high-order multilevel optimization strategies
Henri Calandra, Serge Gratton, Elisa Riccietti +1
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order…
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method
Henri Calandra, Serge Gratton, Elisa Riccietti +1
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used t…
Minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity
S. Gratton, E. Simon, Ph. L. Toint
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that…