LEADER 03751nam 22005655 450 001 9910364956703321 005 20200630005337.0 010 $a3-030-35554-3 024 7 $a10.1007/978-3-030-35554-8 035 $a(CKB)4100000010011899 035 $a(MiAaPQ)EBC5997306 035 $a(DE-He213)978-3-030-35554-8 035 $a(PPN)24281882X 035 $a(EXLCZ)994100000010011899 100 $a20191216d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTensor Spaces and Numerical Tensor Calculus /$fby Wolfgang Hackbusch 205 $a2nd ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (622 pages) 225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v56 311 $a3-030-35553-5 327 $aPart I: Algebraic Tensors -- 1 Introduction -- 2 Matrix Tools -- 3 Algebraic Foundations of Tensor Spaces -- Part II: Functional Analysis of Tensor Spaces -- 4 Banach Tensor Spaces -- 5 General Techniques -- 6 Minimal Subspaces -- Part III: Numerical Treatment -- 7 r-Term Representation -- 8 Tensor Subspace Represenation -- 9 r-Term Approximation -- 10 Tensor Subspace Approximation -- 11 Hierarchical Tensor Representation -- 12 Matrix Product Systems -- 13 Tensor Operations -- 14 Tensorisation -- 15 Multivariate Cross Approximation -- 16 Applications to Elliptic Partial Differential Equations -- 17 Miscellaneous Topics. 330 $aSpecial numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra. 410 0$aSpringer Series in Computational Mathematics,$x0179-3632 ;$v56 606 $aNumerical analysis 606 $aChemistry, Physical and theoretical 606 $aMathematical physics 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aTheoretical and Computational Chemistry$3https://scigraph.springernature.com/ontologies/product-market-codes/C25007 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aNumerical analysis. 615 0$aChemistry, Physical and theoretical. 615 0$aMathematical physics. 615 14$aNumerical Analysis. 615 24$aTheoretical and Computational Chemistry. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a515.63 700 $aHackbusch$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$051792 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910364956703321 996 $aTensor spaces and numerical tensor calculus$9847126 997 $aUNINA