LEADER 03441nam 2200481 450 001 9910819209203321 005 20230814221243.0 010 $a3-11-039139-2 010 $a3-11-036591-X 024 7 $a10.1515/9783110365917 035 $a(CKB)3850000000001082 035 $a(MiAaPQ)EBC4917467 035 $a(DE-B1597)428236 035 $a(OCoLC)1042026708 035 $a(DE-B1597)9783110365917 035 $a(Au-PeEL)EBL4917467 035 $a(CaPaEBR)ebr11605309 035 $a(EXLCZ)993850000000001082 100 $a20180921d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTensor numerical methods in scientific computing /$fBoris N. Khoromskij 210 1$aBerlin ;$aMunich ;$aBoston :$cDe Gruyter,$d[2018] 210 4$dİ2018 215 $a1 online resource (382 pages) 225 0 $aRadon Series on Computational and Applied Mathematics ;$v19 311 $a3-11-037013-1 327 $tFrontmatter -- $tContents -- $t1. Introduction -- $t2. Theory on separable approximation of multivariate functions -- $t3. Multilinear algebra and nonlinear tensor approximation -- $t4. Superfast computations via quantized tensor approximation -- $t5. Tensor approach to multidimensional integrodifferential equations -- $tBibliography -- $tIndex 330 $aThe 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 606 $aCalculus of tensors 615 0$aCalculus of tensors. 676 $a515.63 700 $aKhoromskij$b Boris N.$01648769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819209203321 996 $aTensor numerical methods in scientific computing$93997163 997 $aUNINA