000 | 02864nam a22004815i 4500 | ||
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001 | 978-3-642-28027-6 | ||
003 | DE-He213 | ||
005 | 20140220083310.0 | ||
007 | cr nn 008mamaa | ||
008 | 120223s2012 gw | s |||| 0|eng d | ||
020 |
_a9783642280276 _9978-3-642-28027-6 |
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024 | 7 |
_a10.1007/978-3-642-28027-6 _2doi |
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050 | 4 | _aQA297-299.4 | |
072 | 7 |
_aPBKS _2bicssc |
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072 | 7 |
_aMAT021000 _2bisacsh |
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072 | 7 |
_aMAT006000 _2bisacsh |
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082 | 0 | 4 |
_a518 _223 |
100 | 1 |
_aHackbusch, Wolfgang. _eauthor. |
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245 | 1 | 0 |
_aTensor Spaces and Numerical Tensor Calculus _h[electronic resource] / _cby Wolfgang Hackbusch. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012. |
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300 |
_aXXIV, 500p. 9 illus., 3 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSpringer Series in Computational Mathematics, _x0179-3632 ; _v42 |
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505 | 0 | _aPart I: Algebraic Tensors -- Introduction -- Matrix Tools -- Algebraic Foundations of Tensor Spaces -- Part II: Functional Analysis of Tensor Spaces -- Banach Tensor Spaces -- General Techniques -- Minimal Subspaces.-Part III: Numerical Treatment -- r-Term Representation -- Tensor Subspace Represenation -- r-Term Approximation -- Tensor Subspace Approximation.-Hierarchical Tensor Representation -- Matrix Product Systems -- Tensor Operations -- Tensorisation -- Generalised Cross Approximation -- Applications to Elliptic Partial Differential Equations -- Miscellaneous Topics -- References -- Index. | |
520 | _aSpecial numerical techniques are already needed to deal with nxn matrices for large n. Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. | ||
650 | 0 | _aMathematics. | |
650 | 0 | _aChemistry. | |
650 | 0 | _aNumerical analysis. | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aNumerical Analysis. |
650 | 2 | 4 | _aTheoretical and Computational Chemistry. |
650 | 2 | 4 | _aTheoretical, Mathematical and Computational Physics. |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642280269 |
830 | 0 |
_aSpringer Series in Computational Mathematics, _x0179-3632 ; _v42 |
|
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-642-28027-6 |
912 | _aZDB-2-SMA | ||
999 |
_c102705 _d102705 |