1# Library to Find Best eBook for Read
Author : Boris Khoromskij
Release : 2016
Genre :
Kind : eBook
Book Rating : 924/5 ( reviews)
Book Synopsis Tensor Numerical Methods in Scientific Computing by : Boris Khoromskij
Download or read book Tensor Numerical Methods in Scientific Computing written by Boris Khoromskij. This book was released on 2016. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Boris N. Khoromskij
Release : 2018-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 91X/5 ( reviews)
Book Synopsis Tensor Numerical Methods in Scientific Computing by : Boris N. Khoromskij
Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij. This book was released on 2018-06-11. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Venera Khoromskaia
Release : 2018-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 376/5 ( reviews)
Book Synopsis Tensor Numerical Methods in Quantum Chemistry by : Venera Khoromskaia
Download or read book Tensor Numerical Methods in Quantum Chemistry written by Venera Khoromskaia. This book was released on 2018-06-11. Available in PDF, EPUB and Kindle. Book excerpt: The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.
Author : Boris N. Choromskij
Release : 2010
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Tensors-structured Numerical Methods in Scientific Computing by : Boris N. Choromskij
Download or read book Tensors-structured Numerical Methods in Scientific Computing written by Boris N. Choromskij. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing. The guiding principle of the tensor methods is an approximation of multivariate functions and operators relying on certain separation of variables. Along with the traditional canonical and Tucker models, we focus on the recent quantics-TT tensor approximation method that allows to represent N-d tensors with log-volume complexity, O(dlog N). We outline how these methods can be applied in the framework of tensor truncated iteration for the solution of the high-dimensional elliptic/parabolic equations and parametric PDEs. Numerical examples demonstrate that the tensor-structured methods have proved their value in application to various computational problems arising in quantum chemistry and in the multi-dimensional/parametric FEM/BEM modelingthe tool apparently works and gives the promise for future use in challenging high-dimensional applications.
Author : P.G. Ciarlet
Release : 1990
Genre : Computers
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Techniques of Scientific Computing (Part 1) - Solution of Equations in Rn by : P.G. Ciarlet
Download or read book Techniques of Scientific Computing (Part 1) - Solution of Equations in Rn written by P.G. Ciarlet. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt:
