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Titlebook: Extraction of Quantifiable Information from Complex Systems; Stephan Dahlke,Wolfgang Dahmen,Harry Yserentant Book 2014 Springer Internatio

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書(shū)目名稱Extraction of Quantifiable Information from Complex Systems
編輯Stephan Dahlke,Wolfgang Dahmen,Harry Yserentant
視頻videohttp://file.papertrans.cn/320/319965/319965.mp4
叢書(shū)名稱Lecture Notes in Computational Science and Engineering
圖書(shū)封面Titlebook: Extraction of Quantifiable Information from Complex Systems;  Stephan Dahlke,Wolfgang Dahmen,Harry Yserentant Book 2014 Springer Internatio
描述In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challeng
出版日期Book 2014
關(guān)鍵詞complex systems; computational stochastics; high-dimensional problems; numerical analysis; partial diffe
版次1
doihttps://doi.org/10.1007/978-3-319-08159-5
isbn_softcover978-3-319-34601-4
isbn_ebook978-3-319-08159-5Series ISSN 1439-7358 Series E-ISSN 2197-7100
issn_series 1439-7358
copyrightSpringer International Publishing Switzerland 2014
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Allan MacLean,Pernille Marqvardsen. In this review, we discuss several strategies for an adaptive approximation of tensors in the hierarchical format by black box type techniques, including problems of tensor reconstruction and tensor completion.
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A Review on Adaptive Low-Rank Approximation Techniques in the Hierarchical Tensor Format,. In this review, we discuss several strategies for an adaptive approximation of tensors in the hierarchical format by black box type techniques, including problems of tensor reconstruction and tensor completion.
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ESG Factors in the Investment Processc concept of subspace approximation and higher order SVD (HOSVD), and how to extend this in a hierarchical way. We highlight that the present tensor representations are constituting smooth manifolds, and give a perspective how these properties can be used to develop numerical solvers for tensor equations and tensor optimisation problems.
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