title: On Monte Carlo method in distributed memory systems
metadata.name: dc.contributor.author
metadata.value: Ermakov, Sergey M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Trosinenko, Anatolii V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-01-05T17:49:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T17:49:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov S.M., Trosinenko A. V. On Monte Carlo method in distributed memory systems. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 558–569.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5896
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The work is devoted to solving systems of linear algebraic equations on distributed memory computers. It is
  supposed that there are M computing nodes, each of which has a limited fast memory, and communication
  between nodes takes considerable time.
  Provided that the matrix elements and vector of the right side can not be placed in its entirety in the
  memory of one node, the problem of effective use of equipment in between exchanges, i.e. whether each
  node to use the data available to him to be able to reduce the overall residual. In general assumptions
  about the matrix of the answer to this question is negative. An example is placed in the Appendix.
  We consider the case when the system has a large enough order and appropriate to apply the Monte
  Carlo method, the matrix is divided between computing nodes on non-overlapping blocks of rows with the
  same partition into blocks of indices of rows and columns. We also consider a modification of the method
  of simple iteration, based on this partition, consisting of two nested iterative process, so that only the
  outer iteration involve the exchange of messages between nodes.
  This iterative process leads naturally to a similar process using the Monte Carlo method that does
  not require a full copy of the storage matrix of the system on each compute node.
  The paper constructed and investigated for solving the linear estimates for the case and under certain
  additional conditions on the matrix system proved sufficient conditions for convergence. Refs 8.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №14-01-00271-а).
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Monte Carlo method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: parallel computation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asynchronous iterative method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On Monte Carlo method in distributed memory systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05-Ermakov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5896/1/05-Ermakov.pdf
resources.format: Adobe PDF
resources.size: 277,49 kB