Asymptotically optimal designs on compact algebraic manifolds

We find $t$-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree $t$ on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of special interest is the particular case of the Grassmann...

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Detalles Bibliográficos
Autores: Etayo, Ujué, Marzo Sánchez, Jordi, Ortega Cerdà, Joaquim
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/127174
Acceso en línea:https://hdl.handle.net/2445/127174
Access Level:acceso abierto
Palabra clave:Expansions asimptòtiques
Teoria de l'aproximació
Geometria discreta
Asymptotic expansions
Approximation theory
Discrete geometry
Descripción
Sumario:We find $t$-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree $t$ on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of special interest is the particular case of the Grassmannians where our results improve the bounds that had been proved previously.