A complex homographic best approximation problem. Application to Optimized Robin-Schwarz algorithms, and optimal control problems

Bérangère Delourme (1) , Laurence Halpern (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Homographic complex best approximation has emerged in the last years, as an essential tool for the design of new, performant domain decomposition Robin-Schwarz algorithms. We present and analyse a fully complex problem, introducing a new alternation property. We give operational formulas for the solution, and apply them to a control problem.

Mots clés: Domain decomposition; Complex best approximation; Optimal control; Schwarz algorithms

Domaines: Analyse numérique [math.NA]

Bérangère Delourme, Laurence Halpern. A complex homographic best approximation problem. Application to Optimized Robin-Schwarz algorithms, and optimal control problems. 2021. ⟨hal-02554807v2⟩