title: Backward iterations for solving integral equations with polynomial nonlinearity
metadata.name: dc.contributor.author
metadata.value: Ermakov, Sergey M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Surovikina, Tamara O.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-04-14T11:01:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-04-14T11:01:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov S.M., Surovikina T.O. Backward iterations for solving integral equations with polynomial nonlinearity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 1, pp. 23–36.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.103
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36151
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The theory of adjoint operators is widely used in solving applied multidimensional problems with Monte Carlo method. Efficient algorithms are constructed using the duality principle for many problems described in linear integral equations of the second kind. On the other hand, important applications of adjoint equations for designing experiments were suggested by G.Marchuk and his colleagues in their respective works. Some results obtained in these fields are also generalized to the case of nonlinear operators. Linearization methods were mostly used for that purpose. Results for Lyapunov-Schmidt nonlinear polynomial equations were obtained in the theory of Monte Carlo methods. However, many interesting questions in this subject area are remained open. New results about dual processes used for solving polynomial equations with Monte Carlo method are presented. In particular, an adjoint Markov process for the branching process and the corresponding unbiased estimate of the functional of the solution to the equation are constructed in a general form. The possibility of constructing an adjoint operator to a nonlinear one is discussed.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Monte Carlo method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dual estimate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov - Schmidt nonlinear equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: balance equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: adjoint equations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Backward iterations for solving integral equations with polynomial nonlinearity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 23-36.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36151/1/23-36.pdf
resources.format: Adobe PDF
resources.size: 341,64 kB