Academic Journal
Tensor Numerical Methods: Actual Theory and Recent Applications.
| Τίτλος: | Tensor Numerical Methods: Actual Theory and Recent Applications. |
|---|---|
| Συγγραφείς: | Gavrilyuk, Ivan, Khoromskij, Boris N. |
| Πηγή: | Computational Methods in Applied Mathematics; Jan2019, Vol. 19 Issue 1, p1-4, 4p |
| Θεματικοί όροι: | Big data, Mathematical models, Stochastic processes |
| Περίληψη: | Most important computational problems nowadays are those related to processing of the large data sets and to numerical solution of the high-dimensional integral-differential equations. These problems arise in numerical modeling in quantum chemistry, material science, and multiparticle dynamics, as well as in machine learning, computer simulation of stochastic processes and many other applications related to big data analysis. Modern tensor numerical methods enable solution of the multidimensional partial differential equations (PDE) in ℝ d {\mathbb{R}^{d}} by reducing them to one-dimensional calculations. Thus, they allow to avoid the so-called "curse of dimensionality", i.e. exponential growth of the computational complexity in the dimension size d, in the course of numerical solution of high-dimensional problems. At present, both tensor numerical methods and multilinear algebra of big data continue to expand actively to further theoretical and applied research topics. This issue of CMAM is devoted to the recent developments in the theory of tensor numerical methods and their applications in scientific computing and data analysis. Current activities in this emerging field on the effective numerical modeling of temporal and stationary multidimensional PDEs and beyond are presented in the following ten articles, and some future trends are highlighted therein. [ABSTRACT FROM AUTHOR] |
| Copyright of Computational Methods in Applied Mathematics is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Tensor Numerical Methods: Actual Theory and Recent Applications. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gavrilyuk%2C+Ivan%22">Gavrilyuk, Ivan</searchLink><br /><searchLink fieldCode="AR" term="%22Khoromskij%2C+Boris+N%2E%22">Khoromskij, Boris N.</searchLink> – Name: TitleSource Label: Source Group: Src Data: Computational Methods in Applied Mathematics; Jan2019, Vol. 19 Issue 1, p1-4, 4p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Big+data%22">Big data</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Most important computational problems nowadays are those related to processing of the large data sets and to numerical solution of the high-dimensional integral-differential equations. These problems arise in numerical modeling in quantum chemistry, material science, and multiparticle dynamics, as well as in machine learning, computer simulation of stochastic processes and many other applications related to big data analysis. Modern tensor numerical methods enable solution of the multidimensional partial differential equations (PDE) in ℝ d {\mathbb{R}^{d}} by reducing them to one-dimensional calculations. Thus, they allow to avoid the so-called "curse of dimensionality", i.e. exponential growth of the computational complexity in the dimension size d, in the course of numerical solution of high-dimensional problems. At present, both tensor numerical methods and multilinear algebra of big data continue to expand actively to further theoretical and applied research topics. This issue of CMAM is devoted to the recent developments in the theory of tensor numerical methods and their applications in scientific computing and data analysis. Current activities in this emerging field on the effective numerical modeling of temporal and stationary multidimensional PDEs and beyond are presented in the following ten articles, and some future trends are highlighted therein. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Computational Methods in Applied Mathematics is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1515/cmam-2018-0014 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 4 StartPage: 1 Subjects: – SubjectFull: Big data Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Stochastic processes Type: general Titles: – TitleFull: Tensor Numerical Methods: Actual Theory and Recent Applications. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gavrilyuk, Ivan – PersonEntity: Name: NameFull: Khoromskij, Boris N. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 16094840 Numbering: – Type: volume Value: 19 – Type: issue Value: 1 Titles: – TitleFull: Computational Methods in Applied Mathematics Type: main |
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