000 02864nam a22004815i 4500
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
024 7 _a10.1007/978-3-642-28027-6
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aHackbusch, Wolfgang.
_eauthor.
245 1 0 _aTensor Spaces and Numerical Tensor Calculus
_h[electronic resource] /
_cby Wolfgang Hackbusch.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aXXIV, 500p. 9 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Computational Mathematics,
_x0179-3632 ;
_v42
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