HDAD
Financiado
High Dimensional Approximation and Discretization
Approximation and discretization are two steps of making high dimensional problems more computationally feasible. On the one hand, both the approximation of certain functional classes by simpler functions and the discretization of...
Approximation and discretization are two steps of making high dimensional problems more computationally feasible. On the one hand, both the approximation of certain functional classes by simpler functions and the discretization of underlying space while preserving certain important properties are classical problems. On the other hand, new trends and challenges in pure mathematics and applications lead to new approximation and discretization problems.
The main goal of this research is to study certain high dimensional approximation and discretization problems. Firstly, we intend to obtain new innovative results in the problem of integral norms discretization both in the important special case of algebraic polynomials on convex domains and in the general case of any finite dimensional subspace of continuous functions. Secondly, we will study the dependence of the rate of approximation by polynomials on the smoothness properties of functions. While this second problem itself is classical our main aim is to study it in new settings. Finally, both described problems will require the study of various properties of multivariate algebraic polynomials.
The stated goals require the development of a new technique involving a combination of classical analytic and new probabilistic approaches. In order to develop this new technique, the researcher will work under the supervision of Sergey Tikhonov, who is one of the most experienced researchers in the fields of harmonic analysis, approximation, and discretization. While working with the supervisor, the researcher will acquire techniques of classical approximation theory. Then this new obtained techniques will be combined with the researcher's own expertise in probabilistic approaches in functional analysis.
In conclusion, this MSC fellowship will allow the applicant to obtain new important results in various research areas. This will support him as an independent researcher and advance his career opportunities within the EU.
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Duración del proyecto: 27 meses
Fecha Inicio: 2023-05-04
Fecha Fin: 2025-08-31
Fecha Fin: 2025-08-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-05-04
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2022-PF-01-01:
MSCA Postdoctoral Fellowships 2022
Cerrada
hace 2 años
Presupuesto
El presupuesto total del proyecto asciende a
165K€
Líder del proyecto
CONSORCI CENTRE DE RECERCA MATEMATICA
Otra investigación y desarrollo experimental en ciencias naturales y técnicas otros tipos
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5