Tensor Numerical Methods in Scientific Computing by Boris N Khoromskij
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 (QT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FT 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 QT 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-
Lectures on Advanced Computational Methods in Mechanics
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Grobner Bases in Control Theory and Signal Processing
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Topological Optimization and Optimal Transport
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Variational Methods
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Optimization and Control for Partial Differential Equations
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Grobner Bases in Symbolic Analysis
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Direct and Inverse Problems in Wave Propagation and Applications
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Multiphysics Phase-Field Fracture
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Fluid-Structure Interaction
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Multivariate Algorithms and Information-Based Complexity
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Hamilton-Jacobi-Bellman Equations
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Simulation of Flow in Porous Media
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Large Scale Inverse Problems
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Finite Fields and Their Applications
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Regularization Methods in Banach Spaces
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Combinatorics and Finite Fields
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Discrepancy Theory
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Space-Time Methods
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The Radon Transform
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Maxwells Equations
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Uniform Distribution and Quasi-Monte Carlo Methods
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Algebraic Curves and Finite Fields
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Robust Static Super-Replication of Barrier Options
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Theoretical Foundations and Numerical Methods for Sparse Recovery
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Robust Algebraic Multilevel Methods and Algorithms
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A Posteriori Estimates for Partial Differential Equations
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Advanced Financial Modelling
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Iterative Regularization Methods for Nonlinear Ill-Posed Problems
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Inverse Problems on Large Scales
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Microlocal Analysis and Inverse Problems in Tomography and Geometry
Boris N. Khoromskij, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany.
| SKU | Unavailable |
| ISBN 13 | 9783110370133 |
| ISBN 10 | 3110370131 |
| Title | Tensor Numerical Methods in Scientific Computing |
| Author | Boris N Khoromskij |
| Series | Radon Series On Computational And Applied Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | De Gruyter |
| Year published | 2018-06-11 |
| Number of pages | 379 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |