Project description
New approaches to function approximation and discretisation
High-dimensional problems in mathematics often involve complex functions and vast spaces that are difficult to compute. To make these problems more manageable, it is necessary to simplify functions and discretise spaces while preserving their important properties. The need for more effective techniques is pressing as problems become increasingly intricate. With the support of the Marie Skłodowska-Curie Actions programme, the HDAD project aims to enhance integral norms discretisation for algebraic polynomials on convex domains and extend this to any finite-dimensional subspace of continuous functions. Additionally, the project will explore how polynomial approximation rates vary with function smoothness. Overall, the research will integrate classical analytic and novel probabilistic approaches, aiming to produce groundbreaking results and advance the researcher’s career.
Objective
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.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2022-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
08193 Bellaterra
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.