Seminari del Dipartimento di Matematica

Seminario del 2026

Ludovico Bruni Bruno

Unconventional approximation: histopolation

analisi numerica

Histopolation is an approximation procedure that replaces nodal evaluations with weaker functionals, such as integral data or averages. Histopolation naturally appears in many branches of numerical analysis: from finite volumes, finite elments and mimetic schemes to preconditioning. Despite this, histopolation is lesser-known than the more celebrated interpolation, mostly due to the lack of an approximation-theoretical approach in a classical sense. In fact, the definition and characterization of a Lebesgue constant for histopolation-based problems only dates back to 2024. It is thus after that year that such a machinery gained new interest and consolidated as an appropriate alternative to more popular projection techniques, such as interpolation or moments-based methods. In this talk we review the most important instances of histopolation, with a perspective on the well-posedness of the problem, its conditioning and its most relevant applications.