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Mathematics

OUR RESEARCH FOCUS

We investigate various problems in mathematical analysis. More precisely we are interested in functional analysis, operator theory, geometric analysis and probability theory, in many instances combinations of these fields. Our results find their applications in optimization and averaging of datasets within nonlinear structures. Practical applications include medical imaging tools, control theory, radar technology, learning algorithms in artifical intelligence and qantum information systems.

Mid-term budgetary forecast – project

We aim to investigate extension of basic theorems and optimization techniques of probability calculus to nonlinear structures. We combined the theory of gradient currents and operator semigroups with tools of geometric analysis in order to construct discrete-time gradient currents, and then observe their convergence. We have succeeded in constructing an algorithm that approximates the zero position of nonlinear operators in a rather general and abstract space (Thompson metric spaces). A nonlinear generalisation of the law of large numbers emerged as a special case of the convergence of the stochastic algorithm. The results obtained demonstrate that the gradient currents converge to the zero point of the generating nonlinear operator. This can be considered a kind of gradient method, for example, it can be used to average matrices. Furthermore, several interesting minimisation problems can be written in a form where the gradient of the function in question gives the nonlinear operator, whose zeros are the critical points.

Corvinus University of Budapest

MEMBERS

Head of Research Center

Vince Dániel

Léka Zoltán (Óbuda University)

PUBLICATION HIGHLIGHTS

IMPACT

We actively participate in international research projects (National Research Foundation of Korea-NRF grant funded by the Korea government No.2015R1A3A2031159) and in national research groups with the support provided by the Ministry of Innovation and Technology of Hungary from the National (TKP2021-NVA-09).

Contact us for cooperation

miklos.palfia@uni-corvinus.hu

 

Previous partnerships

Óbuda University

Departamento de de Matematica, La Plata, Argentina

Instituto Argentino de Matematica, `Alberto P. Calderon’, Argentina.

Sungkyunkwan University, Korea

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GEN.:2024.07.20. - 02:53:16