3 papers
math.NA2026
Convergence Analysis of the Random Bisection Method
Ludovick Bouthat, Philippe-André Luneau, Philippe Petitclerc
We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute ex…
math.NA2025
General Framework and Error Estimates for ROM-accelerated Fixed Point Iterations
Philippe-André Luneau, Jean Deteix
Whether it is for solving nonlinear equations, optimization problems, or autonomous dynamical systems, fixed-point-type iterations are widely used in numerical sciences. On-the-fly…
math.NA2024
Conservative Surrogate Models for Optimization with the Active Subspace Method
Philippe-André Luneau
We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of th…