Tensor Numerical Methods in Scientific Computing / / Boris N. Khoromskij.
The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximati...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2018] ©2018 |
Year of Publication: | 2018 |
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Khoromskij, Boris N., author. aut http://id.loc.gov/vocabulary/relators/aut Tensor Numerical Methods in Scientific Computing / Boris N. Khoromskij. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (369 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Radon Series on Computational and Applied Mathematics , 1865-3707 ; 19 Frontmatter -- Contents -- 1. Introduction -- 2. Theory on separable approximation of multivariate functions -- 3. Multilinear algebra and nonlinear tensor approximation -- 4. Superfast computations via quantized tensor approximation -- 5. Tensor approach to multidimensional integrodifferential equations -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Calculus of tensors. Numerik. Tensormethoden. Wissenschaftliches Rechnen. MATHEMATICS / Applied. bisacsh Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 9783110762488 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 9783110719550 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English 9783110604252 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 9783110603255 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English 9783110604191 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 9783110603194 ZDB-23-DMA Title is part of eBook package: De Gruyter Radon Series on Applied Mathematics eBook-Package 9783110647174 EPUB 9783110391398 print 9783110370133 https://doi.org/10.1515/9783110365917 https://www.degruyter.com/isbn/9783110365917 Cover https://www.degruyter.com/document/cover/isbn/9783110365917/original |
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English |
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eBook |
author |
Khoromskij, Boris N., Khoromskij, Boris N., |
spellingShingle |
Khoromskij, Boris N., Khoromskij, Boris N., Tensor Numerical Methods in Scientific Computing / Radon Series on Computational and Applied Mathematics , Frontmatter -- Contents -- 1. Introduction -- 2. Theory on separable approximation of multivariate functions -- 3. Multilinear algebra and nonlinear tensor approximation -- 4. Superfast computations via quantized tensor approximation -- 5. Tensor approach to multidimensional integrodifferential equations -- Bibliography -- Index |
author_facet |
Khoromskij, Boris N., Khoromskij, Boris N., |
author_variant |
b n k bn bnk b n k bn bnk |
author_role |
VerfasserIn VerfasserIn |
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Khoromskij, Boris N., |
title |
Tensor Numerical Methods in Scientific Computing / |
title_full |
Tensor Numerical Methods in Scientific Computing / Boris N. Khoromskij. |
title_fullStr |
Tensor Numerical Methods in Scientific Computing / Boris N. Khoromskij. |
title_full_unstemmed |
Tensor Numerical Methods in Scientific Computing / Boris N. Khoromskij. |
title_auth |
Tensor Numerical Methods in Scientific Computing / |
title_alt |
Frontmatter -- Contents -- 1. Introduction -- 2. Theory on separable approximation of multivariate functions -- 3. Multilinear algebra and nonlinear tensor approximation -- 4. Superfast computations via quantized tensor approximation -- 5. Tensor approach to multidimensional integrodifferential equations -- Bibliography -- Index |
title_new |
Tensor Numerical Methods in Scientific Computing / |
title_sort |
tensor numerical methods in scientific computing / |
series |
Radon Series on Computational and Applied Mathematics , |
series2 |
Radon Series on Computational and Applied Mathematics , |
publisher |
De Gruyter, |
publishDate |
2018 |
physical |
1 online resource (369 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- 1. Introduction -- 2. Theory on separable approximation of multivariate functions -- 3. Multilinear algebra and nonlinear tensor approximation -- 4. Superfast computations via quantized tensor approximation -- 5. Tensor approach to multidimensional integrodifferential equations -- Bibliography -- Index |
isbn |
9783110365917 9783110762488 9783110719550 9783110604252 9783110603255 9783110604191 9783110603194 9783110647174 9783110391398 9783110370133 |
issn |
1865-3707 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA433 |
callnumber-sort |
QA 3433 K467 42018 |
url |
https://doi.org/10.1515/9783110365917 https://www.degruyter.com/isbn/9783110365917 https://www.degruyter.com/document/cover/isbn/9783110365917/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.63 |
dewey-sort |
3515 263 |
dewey-raw |
515/.63 |
dewey-search |
515/.63 |
doi_str_mv |
10.1515/9783110365917 |
oclc_num |
1042026708 |
work_keys_str_mv |
AT khoromskijborisn tensornumericalmethodsinscientificcomputing |
status_str |
n |
ids_txt_mv |
(DE-B1597)428236 (OCoLC)1042026708 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 Title is part of eBook package: De Gruyter Radon Series on Applied Mathematics eBook-Package |
is_hierarchy_title |
Tensor Numerical Methods in Scientific Computing / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 |
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1806144366682570752 |
fullrecord |
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