25 citations · 53 across the 8 of their papers we have counts for
4 papers · 1 filter
On the Exponentiation of Interval Matrices
Alexandre Goldsztejn
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and co…
Manifold approximation of set-valued functions
Alexandre Goldsztejn
A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.
Revisiting the upper bounding process in a safe Branch and Bound algorithm
Alexandre Goldsztejn, Yahia Lebbah, Claude Michel +1
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new str…
A Data-Parallel Algorithm to Reliably Solve Systems of Nonlinear Equations
Frédéric Goualard, Alexandre Goldsztejn
Numerical methods based on interval arithmetic are efficient means to reliably solve nonlinear systems of equations. Algorithm bc3revise is an interval method that tightens variabl…