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    Generation of explicit knowledge from empirical data through pruning of trainable neural networks
[Text]. - Electronic text data (125 Кб)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=1269. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1999/1269gorban_IJCNN99Know.pdf (Полный текст) : статья / A.N. Gorban, Ye.M. Mirkes, V.G. Tsaregorodtsev. - Electronic text data (125 Кб) // Proceedings of International Joint Conference on Neural Networks. - Washington, 1999. - p. 436-441
ГРНТИ

Аннотация: This paper presents a generalized technology of extraction of explicit knowledge from data. The main ideas are 1) maximal reduction of network complexity (not only removal of neurons or synapses, but removal all the unnecessary elements and signals and reduction of the complexity of elements), 2) using of adjustable and flexible pruning process (the pruning sequence shouldn't be predetermined - the user should have a possibility to prune network on his own way in order to achieve a desired network structure for the purpose of extraction of rules of desired type and form), and 3) extraction of rules not in predetermined but any desired form. Some considerations and notes about network architecture and training process and applicability of currently developed pruning techniques and rule extraction algorithms are discussed. This technology, being developed by us for more than 10 years, allowed us to create dozens of knowledge-based expert systems.

http://icm.krasn.ru/refextra.php?id=1269,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Mirkes, Ye.M.; Миркес Е.М.; Tsaregorodtsev, V.G.; Царегородцев, Виктор Геннадьевич; Горбань, Александр Николаевич

    Convergence of a full multigrid algorithm for quadratic finite elements in a domain with a curvilinear boundary
[Text] / L. V. Gileva, V. V. Shaidurov // Russ. J. Numer. Anal. Math. Model. - 2009. - Vol. 24, Is. 5. - P425-438, DOI 10.1515/RJNAMM.2009.027. - Cited References: 11. - This analysis was partially supported by Grant 08-01-00621 of the Russian Foundation of Basic Research. . - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.


Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]

    Solving the linear interval tolerance problem
/ S. P. Shary // Mathematics and Computers in Simulation. - 1995. - Vol. 39, Is. 1-2. - P53-85 . - ISSN 0378-4754

Аннотация: For the interval linear system Ax = b, the linear tolerance problem is considered that requires inner evaluation of the tolerable solution set ???(A, b) = {x ? Rn {divides} (?A ? A)(Ax ? b)} formed by all point vectors x such that the product Ax remains within b for all possible A ? A. Along with the simple incompatibility criterion, we develop comprehensive solvability theory for the linear tolerance problem that not only settles whether ??? is empty or not, but also enables modification of the problem to ensure its desired properties. To conclude, we advance several numerical methods of various accuracy and complexity for construction of an interval solution to the linear tolerance problem around a given center. В© 1995.

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Держатели документа:
Computer Center, Siberian Department, Russian Academy of Sciences, Akademgorodok, 660036 Krasnoyarsk, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Shary, S.P.; Шарый С.П.

    Symmetry of Siberian Larch Transcriptome
[Text] : статья / Michael G. Sadovsky [et al.] // Журнал Сибирского федерального университета. Серия: Биология. - 2015. - Т. 8, № 3. - P278-286, DOI 10.17516/1997-1389-2015-8-3-278-286 . - ISSN 1997-1389
   Перевод заглавия: Симметрия транскриптома сибирской лиственницы
УДК

Аннотация: The paper presents a novel approach to infer a structuredness in a set of symbol sequences such as transcriptome nucleotide sequences. A distribution pattern of triplet frequencies in the Siberian larch (Larix sibirica Ledeb.) transcriptome sequences was investigated in the presented study. It was found that the larch transcriptome demonstrates a number of unexpected symmetries in the statistical and combinatorial properties.
Проанализированы структуры, выделяемые в транскриптоме лиственницы. Показано, что данный набор последовательностей обладает необычной симметрией своих статистических и комбинаторных свойств.

РИНЦ

Держатели документа:
Georg-August-University of Gottingen
Institute of Computational Modelling SB RAS
M University HFSB
N. I. Vavilov Institute of General Genetics RAS
Siberian Federal University Genome Research and Education Centre
Texas A&amp
V. N. Sukachev Institute of Forest SB RAS

Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Birukov, Vladislav V.; Бирюков В.В.; Putintseva, Yuliya A.; Путинцева Ю.А.; Oreshkova, Nataliya V.; Орешкова Н.В.; Vaganov, Eugene A.; Ваганов Е.А.; Krutovsky, Konstantin V.; Крутовский К.В.

    Seven-Cluster Structure of Larch Chloroplast Genome
[Text] : статья / M. G. Sadovsky [et al.] // Журнал Сибирского федерального университета. Серия: Биология. - 2015. - Т. 8, № 3. - P268-277, DOI 10.17516/1997-1389-2015-8-3-268-277. . - ISSN 1997-1389
   Перевод заглавия: Семикластерная структура генома хлоропласта лиственницы
УДК

Кл.слова (ненормированные):
Chloroplast genome -- complexity -- frequency dictionary -- order -- phase -- triplet -- сложность -- частотный словарь -- порядок -- фаза -- триплет

Аннотация: The paper presents a novel approach to study a nucleotide sequence structure with respect to the chloroplast genome DNA sequence analysis. A speci?c frequencies distribution pattern of the consecutive triple nucleotide fragments was identi?ed in the chloroplast genome DNA sequence, which demonstrated a non-degenerated pattern with seven clusters.
Проанализированы структуры, выделяемые в нуклеотидных последовательностях с помощью анализа распределений фрагментов генома. Показано, что последовательность генома хлоропласта обладает невырожденной семикластерной структурой в распределении таких фрагментов по частотам триплетов.

РИНЦ

Держатели документа:
Georg-August-University of Gottingen
Institute of Computational Modelling SB RAS
M University HFSB
N. I. Vavilov Institute of General Genetics RAS
Siberian Federal University Genome Research and Education Centre
Texas A&amp
V. N. Sukachev Institute of Forest SB RAS

Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Bondar, Eugenia I.; Бондар Е.И.; Putintseva, Yulia A.; Путинцева Ю.А.; Oreshkova, Natalia V.; Орешкова Н.В.; Vaganov, Eugene A.; Ваганов Е.А.; Krutovsky, Konstantin V.; Крутовский К.В.

    Алгоритм переменной структуры с применением трехстадийных методов типа Рунге - Кутты и Розенброка
[Текст] : статья / Е. А. Новиков // Известия высших учебных заведений. Поволжский регион. Физико-математические науки. - 2015. - № 3. - С. 50-60 . - ISSN 2072-3040
   Перевод заглавия: Variable structure algorithm applying 3-stage methods of Runge-Kutta and Rosenbrock types
УДК

Аннотация: Актуальность и цели. Проблема решения задачи Коши для жестких систем большой размерности возникает при моделировании физических и химических процессов, при аппроксимации уравнений в частных производных системой обыкновенных дифференциальных уравнений и во многих других важных приложениях. Учет большого числа факторов при построении математических моделей приводит к расширению класса задач, описываемых жесткими системами большой размерности. Сложность практических задач приводит к возрастающим требованиям к вычислительным алгоритмам. Материалы и методы. В случае большой размерности жесткой системы дифференциальных уравнений основные затраты приходятся на декомпозицию матрицы Якоби. В некоторых алгоритмах применяется замораживание матрицы Якоби, т.е. одна матрица используется на нескольких шагах интегрирования. Проблема замораживания матрицы достаточно просто решается в методах, в которых стадии вычисляются с применением итерационного процесса. Для безытерационных численных формул это существенная проблема. В данной работе сокращение затрат достигается за счет комбинирования явных и L -устойчивых методов по критерию устойчивости в процессе расчетов. Результаты. Создан алгоритм интегрирования переменной структуры на основе явной схемы типа Рунге - Кутты и L -устойчивого метода типа Розенброка третьего порядка. На каждом шаге эффективная численная формула выбирается по критерию устойчивости. Оценка максимального собственного числа матрицы Якоби, необходимая для переключения между методами, для явных численных схем определяется степенным методом через ранее вычисленные стадии, а для метода типа Розенброка - через норму матрицы Якоби. Построены неравенства для контроля точности и устойчивости. Приведены результаты расчетов. Выводы. Алгоритм интегрирования предназначен для решения жестких задач большой размерности. Результаты расчетов подтверждают эффективность построенного алгоритма.
Background. The Cauchy problem for large-scale stiff systems arises in simulation of physical and chemical processes, in approximation of partial differential equations by a system of ordinary differential equations and in plenty of other important applications. Taking into consideration a large number of factors in model development leads to expansion of a class of problems, determined by stiff systems of high dimension. The complexity of practical problems leads to additional requirements to computational algorithms. Materials and methods. Dealing with high dimensionality of a stiff system of ordinary differential equations, the main computational expenses concern the Jacobi matrix decomposition. In some algorithms one may use freezing of the Jacobi matrix, i.e. applying the same matrix over several integration steps. The problem of freezing is solved rather easy in those methods, the stages of which are computed using some iterative processes. For non-iterative numerical formulas the freezing is quite a difficult problem. In this study, the costs reduction was achieved by combining explicit and L-stable methods using the criterion of stability in calculations. Results. The author has created an algorithm of variable structure integration, based on the explicit scheme of the Runge-Kutta type and the L-stable method of the Rosenbrock type. Both schemes have the third order of accuracy. An efficient numerical formula was chosen according to the criterion of stability at each step of integration. Estimation of maximum eigen value, which is necessary to switch between the methods, for explicit numerical schemes was determined by power iterations using already computed stages, and using the Jacobi matrix norm for the Rosenbrock type method. The researcher also formulated inequalities for accuracy and stability control. The article adduces the results of calculations. Conclusions. The integration algorithm is aimed at solving stiff problems of high dimension. Numerical results confirm the efficiency of the constructed algorithm.

РИНЦ,
Полный текст

Держатели документа:
Институт вычислительного моделирования Сибирского отделения РАН

Доп.точки доступа:
Novikov E.A.

    Multistable states in the biosphere-climate system: towards conceptual models
/ S. Bartsev, P. Belolipetskii, A. Degermendzhi // V INTERNATIONAL WORKSHOP ON MATHEMATICAL MODELS AND THEIR APPLICATIONS : IOP PUBLISHING LTD, 2017. - Vol. 173: 5th International Workshop on Mathematical Models and their Applications (NOV 07-09, 2016, Krasnoyarsk, RUSSIA). - Ст. UNSP 012005. - (IOP Conference Series-Materials Science and Engineering), DOI 10.1088/1757-899X/173/1/012005. - Cited References:31. - This work was supported by grant RFBR-KKFN No 15-41-04300 and Complex Program of SB RAS No II.2. No 0360-2015-0002. . -
РУБ Materials Science, Multidisciplinary + Mathematics, Applied

Аннотация: Forecasting response of the biosphere and regional ecosystems to observed and expected climate change is the fundamental problem with obvious practical significance. Fundamental non-linearity of the climate system and biosphere makes feasible implementing multiple states and threshold processes in the biosphere-climate system (BCS) in response to gradually increasing influence factor (greenhouse gas concentrations growth). Really time series analysis of global temperature and other global and local parameters indicates the presence of abrupt transitions between stationary states. Identification of the switching mechanisms using general circulation models of the atmosphere and the ocean is associated with the obvious difficulties due to their complexity. Understanding the nature of such switches at qualitative level can be achieved by using a conceptual small-scale models. Some variants of possible mechanisms capable of generating these shifts and simultaneously supporting quasi-stationary periods between them are discussed.

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Держатели документа:
Inst Biophys SB RAS, Krasnoyarsk Sci Ctr, Krasnoyarsk, Russia.
Inst Computat Modelling SB RAS, Krasnoyarsk Sci Ctr, Krasnoyarsk, Russia.

Доп.точки доступа:
Belolipetskii, P.V.; Белолипецкий, Павел Викторович; Degermendzhi, A.; RFBR-KKFN [15-41-04300]; Complex Program of SB RAS [II.2, 0360-2015-0002]

    A semi-Lagrangian numerical method for the three-dimensional advection problem with an isoparametric transformation of subdomains
/ V. Shaydurov, A. Vyatkin, E. Kuchunova // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P599-607, DOI 10.1007/978-3-319-57099-0_68 . -
Аннотация: We develop a semi-Lagrangian algorithm for solving the three-dimensional advection problem. A numerical solution is determined on a uniform cubic grid as a piecewise trilinear function. The method is based on the integral balance equation between two neighboring time levels. The domain of integration at the previous time level is a curved cuboid. To compute an integral over this domain numerically, we approximate this cuboid by another one with the same 8 vertices. The latter cuboid is obtained by a trilinear (isoparametric) transformation of the unit cube. This leads to the integration over the unit cube with the help of the composite midpoint rule. Such a technique provides the validity of the local balance equation and does not involve computational and algorithmic complexity for solving the three-dimensional problem. The numerical experiments confirm the first-order convergence. © Springer International Publishing AG 2017.

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Держатели документа:
Institute of Computational Modelling of SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Siberian Federal University, 79 Svobodny pr, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Vyatkin, A.V.; Вяткин, Александр Владимирович; Kuchunova, E.; Шайдуров, Владимир Викторович

    Временная динамика структурных и функциональных характеристик енисейского фитопланктона в нижнем бьефе Красноярской ГЭС
[Текст] : научное издание / Юлия Андреевна Пономарева, Полина Владимировна Постникова // Вестник Томского государственного университета. Биология. - 2017. - № 38. - С. 167-182, DOI 10.17223/19988591/38/10 . - ISSN 1998-8591
   Перевод заглавия: Temporal dynamics of structural and functional characteristics of the Yenisei river phytoplankton downstream of the Krasnoyarsk hydroelectric power station
Аннотация: Представлены результаты изучения формирования фитопланктонного сообщества и флуоресцентных характеристик вод в условиях сброса высоконапорной Красноярской ГЭС. Сезонные и межгодовые изменения фитопланктона оценивали на основе численности и биомассы клеток фитопланктона, а также концентрации хлорофилла а. Выявлены закономерности сезонных сукцессий и межгодовых вариаций структурно-функциональных характеристик фитопланктона. Обнаружено, что основу флористического списка в реке Енисей составляют диатомовые водоросли (66% от общего видового состава), преобладающие в планктоне во все сезоны года. Наибольший вклад в общую численность и биомассу фитопланктона вносят нанофитопланктон (2-20 мкм) и микрофитопланктон (20-64 мкм). В комплекс доминантов вранневесенний период входили Diatoma vulgare Bory и Hannaea arcus (Ehrb.) Patr., в летний - Aulacoseira islandica (O. Mull.) Sim. и Cyclotella radiosa (Grun.) Lemm., позднелетний - Fragilaria crotonensis Kitt. Вместе с тем на фоне увеличивающегося видового разнообразия и интенсивного развития водорослей в весенне-летний период отмечен спад концентрации хлорофилла а. Установлено, что во все рассматриваемые годы пики численности и биомассы фитопланктона приходятся на июнь за счет колониальных диатомовых водорослей, попадающих в нижний бьеф со стоком из верхнего бьефа.
The Yenisei River is the biggest waterway in Siberia. In the second half of the 20th century, the Yenisei River was overlapped by dams, and it deeply damaged the natural hydrological, hydrochemical and hydrobiological regimes of the river. As a result of constructing the Krasnoyarsk hydroelectric power station, a significant river component - phytoplankton, which occupies the central place in the formation of the aquatic ecosystem - has changed downstream of the river. In the river, phytoplankton is formed from phytoperiphyton and allochthonous algae, including phytoplankton species of upstream reservoirs. Therefore, knowledge of transformation laws of phytoplankton species composition, which occurs during the regulation of the river flow and formation of reservoirs, may contribute to the development of ideas about changing the aquatic communities. The aim of this research was to explore the formation of phytoplankton under the conditions of water discharge in the Krasnoyarsk HPS and to study chlorophyll a concentration. We collected phytoplankton samples at a distance of 34 km below the Krasnoyarsk HPS (55°59'1.8"N, 92°47'13.4"E) in 2008-2014 and analyzed them according standard hydrobiological methods (See Table). In 2012-2014, we measured fluorescent water characteristics along with the study of algae. We took the nomenclature for algae considering taxonomic transformations according to the system adopted by the International algae database (http://www.algaebase.org). A quantitative processing of phytoplankton samples was conducted daily, species composition and biomass of algae was determined weekly. In size, algae cells were differentiated according to Rainey. The degree of complexity of phytoplankton communities was determined calculating the Shannon species diversity index (by biomass). The dominant algae included species making the main contribution into the total phytoplankton biomass. In 20122014, along with the study of algae, we determined chlorophyll а concentration by fluorimetric method, weekly (See Fig. 3). We collected and processed a total of 2453 qualitative and quantitative phytoplankton samples for the period of study; 89 samples to determine chlorophyll а content. Altogether, we found 99 species, kinds and forms of algae from 6 groups in the river phytoplankton. In the Yenisei River, diatoms, which predominate in plankton in all seasons, are characterized by the maximum number of species. There is a certain sequence in the appearance of dominant algae. From late April to late May, Diatoma vulgare Bory and Hannaea arcus (Ehrb.) Patr. were recorded in quantities, in June -Aulacoseira islandica (O. Mull.) Sim., in July - Cyclotella radiosa (Grun.) Lemm., in August - Fragilaria crotonensis Kitt. (See Fig. 1). Upstream of the Krasnoyarsk reservoir A. islandica had a dominant position in nephotic cold layer in June, in July and August - C. radiosa; F. crotonensis was a subdominant. It is known that deep water discharge through the dam (18-40 м) is specific for the Krasnoyarsk reservoir. This causes the flow of algae over the dam. In general, the dynamics of the total number and the total biomass of phytoplankton had the form of unimodal curve within the year (with a peak in June) (See Fig. 2). Nanophytoplankton (2-20 mkm) and microphytoplankton (20-64 mkm) made the biggest contribution to the total biomass of phytoplankton. We recorded peaks of number and biomass of phytoplankton in June in all years in question. We found that the percentage of chlorophyll content per phytoplankton biomass unit had seasonal variations and increased in winter (See Fig. 5). It is known, that the concentration of chlorophyll a depends on dimensional structure of phytoplankton. In spring and summer, the domination of algae cells with bigger volumes in phytoplankton caused a decrease in chlorophyll а concentration.

РИНЦ

Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Пономарева, Юлия Андреевна; Ponomareva Yulia A.; Постникова, Полина Владимировна; Postnikova Polina V.
УДК 550.3
А 45

    Алгоритмы аппроксимации данных специального вида
[Текст] : научное издание / Михаил Александрович Курако, Константин Васильевич Симонов // Информатизация и связь. - 2017. - № 2. - С. 81-87 . - ISSN 2078-8320
   Перевод заглавия: APPROXIMATION ALGORITHMS FOR SPECIAL KIND OF DATA
ББК УДК 550.3

Аннотация: Исследование посвящено разработке алгоритмов для аппроксимации данных наблюдений сложных природных процессов и включает в себя несколько подходов, сочетание которых позволяет аппроксимировать сигналы различной сложности и находить в них скрытые закономерности. Рассматриваемые данные представляют собой данные специ ального вида: наблюдения систем геомониторинга и результаты экспериментальных исследований опасных явлений сейсмической природы. Использование полученной информации о скрытых закономерностях позволяет более эффективно решать задачи восстановления пробелов в данных, экстраполяции сигналов и локального прогноза.
The study focused on the development of algorithms for approximation of observational data of complex natural processes and includes several approaches. The combination of approaches allows to approximate the signals of different complexity and find hidden patterns. The considered data are the data of a special kind: observation of geomonitoring systems and results of experimental studies of natural seismic hazards. The use of the information about the hidden patterns allows you to more effectively solve the problem of recovering gaps in the data, extrapolation of signals and local forecast.

РИНЦ

Держатели документа:
Институт вычислительного моделирования СО РАН
Сибирский федеральный университет

Доп.точки доступа:
Курако, Михаил Александрович; Kurako M.A.; Симонов, Константин Васильевич; Simonov K.V.

    New clusterization method based on graph connectivity search
/ M. G. Sadovsky, E. Y. Bushmelev, A. N. Ostylovsky // J. Sib. Fed. Univ. Math. Phys. - 2017. - Vol. 10, Is. 4. - P443-449, DOI 10.17516/1997-1397-2017-10-4-443-449 . - ISSN 1997-1397

Кл.слова (ненормированные):
Clusterization -- Complexity -- Component -- Connectivity -- Order

Аннотация: New method is proposed to identify clusters in datasets. The method is based on a sequential elimination of the longest distances in dataset, so that the relevant graph looses some edges. The method stops when the graph becomes disconnected. © Siberian Federal University. All rights reserved.

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Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, Russian Federation
Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovsky, M. G.; Bushmelev, E. Y.; Ostylovsky, A. N.
57
Н 76

    Новый метод определения топологии многообразия малой размерности, приближающего многомерныеданные
: статья / Михаил Г. Садовский, Анатолий Н. Остыловский // Журнал Сибирского федерального университета. Серия: Математика и физика. - 2018. - Т. 11, № 3. - С. 322-328, DOI 10.17516/1997-1397-2018-11-3-322-328 . - ISSN 1997-1397
   Перевод заглавия: New Method to Determine Topology of Low-Dimension Manifold Approximating Multidimensional Data Sets
УДК

Кл.слова (ненормированные):
order -- complexity -- clusterization -- complement -- surface genius -- порядок -- сложность -- кластеризация -- компонента -- связность

Аннотация: Представлен новый метод определения особенностей топологии многообразий малой размерности, приближающих многомерные данные. Метод основан на построении дополнения дискретного множества и изучении его особенностей.
New method is proposed to identify topology of a low-dimensional manifold approximating multidimensional datasets. The method is based on the implementation of the compliment for the discrete set of data. Some essential properties and constraints of the method are discussed.

РИНЦ,
Scopus,
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Держатели документа:
Институт вычислительного моделирования СО РАН
Институт математики и фундаментальной информатики Сибирский федеральный университет

Доп.точки доступа:
Садовский, Михаил Г.; Sadovsky Michael G.; Остыловский, Анатолий Н.; Ostylovsky Anatoly N.

    Computation of Mean-Field Equilibria with Correlated Stochastic Processes
/ V. Shaydurov, S. Zhang, V. Kornienko // (11 June 2018 through 16 June 2018 : Springer Verlag, 2019. - Vol. 11386 LNCS. - P468-475, DOI 10.1007/978-3-030-11539-5_54 . -
Аннотация: The numerical algorithm is presented for solving differential problem formulated as the Mean-Field Game (MFG) with the coupled system of two parabolic partial differential equations: the Fokker-Plank-Kolmogorov equation and the Hamilton-Jacobi-Bellman one. The case is considered with correlation of the considered stochastic processes. The description focuses on the discrete semi-Lagrangian approximation of these equations and on the application of the MFG theory directly at discrete level. The constructed algorithm is implemented to the problem of carbon dioxide pollution as an illustration. © 2019, Springer Nature Switzerland AG.

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Держатели документа:
Tianjin University of Finance and Economics, 25# Zhujiang Road, Hexi District, Tianjin, 300222, China
Institute of Computational Modeling of SB RAS, 50/44# Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Siberian Federal University, 79# Svobodnyi Prospect, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Shaydurov, V.; Zhang, S.; Kornienko, V.

    Approximations of two-dimensional Mean Field Games with nonsymmetric controls
/ V. Shaydurov, S. Zhang, V. Kornienko // J. Comput. Appl. Math. - 2020. - Vol. 367. - Ст. 112461, DOI 10.1016/j.cam.2019.112461 . - ISSN 0377-0427
Аннотация: The numerical methods are presented for solving economic problems formulated in the Mean-Field Game (MFG) form. The mean-field equilibrium is a solution of the coupled system of two parabolic partial differential equations: the Fokker–Planck–Kolmogorov equation and the Hamilton–Jacobi–Bellman one. The description focuses on the discrete approximation of these equations and on the application of the MFG theory directly at discrete level. This approach results in an efficient algorithm for finding the corresponding grid control functions. Contrary to other difference schemes, here the semi-Lagrangian approximation is applied, which improves properties of a discrete problem of this type. This implies the fast convergence of an iterative algorithm for the minimization of the cost functional. The constructed algorithms are implemented to the problem of carbon dioxide pollution. © 2019 Elsevier B.V.

Scopus,
Смотреть статью

Держатели документа:
Tianjin University of Finance and Economics, 25, Zhujiang Road, Tianjin, 300222, China
Institute of Computational Modeling of SB RAS, 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Siberian Federal University, 79, Svobodnyi Prospect, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Shaydurov, V.; Zhang, S.; Kornienko, V.