Download or read book Acta Numerica 2014 Volume 23 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2014-06-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
Download or read book Iterative Solution of Large Sparse Systems of Equations written by Wolfgang Hackbusch and published by Springer. This book was released on 2016-06-21 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Download or read book ACTA Numerica 10 Volume Paperback Set written by Arieh Iserles and published by . This book was released on 2017-10-02 with total page 4420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Numerica 1994 Volume 3 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1994-07-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual volume presenting survey papers in numerical analysis accessible to graduate students and researchers. Highlights of the 1994 issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.
Download or read book Hierarchical Matrices Algorithms and Analysis written by Wolfgang Hackbusch and published by Springer. This book was released on 2015-12-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Nature. This book was released on 2019-12-16 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special 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.
Download or read book Acta Numerica written by and published by . This book was released on 1992 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Approximation of the Magnetoquasistatic Model with Uncertainties written by Ulrich Römer and published by Springer. This book was released on 2016-07-27 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.
Download or read book Acta Numerica 1997 Volume 6 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1997-07-10 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.
Download or read book Mathematical Modelling of the Human Cardiovascular System written by Alfio Quarteroni and published by Cambridge University Press. This book was released on 2019-05-09 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.
Download or read book Acta Numerica written by Arieh Iserles and published by ACTA Numerica. This book was released on 2011-09 with total page 3662 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Performance Tensor Computations in Scientific Computing and Data Science written by Edoardo Angelo Di Napoli and published by Frontiers Media SA. This book was released on 2022-11-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Numerica 2016 Volume 25 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2016-08-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
Download or read book Acta Numerica 2020 Volume 29 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2021-01-31 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 475 pages. 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
Download or read book TMS 2014 143rd Annual Meeting Exhibition Annual Meeting Supplemental Proceedings written by The Minerals, Metals & Materials Society (TMS) and published by Springer. This book was released on 2016-12-16 with total page 1152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers present advancements in all aspects of high temperature electrochemistry, from the fundamental to the empirical and from the theoretical to the applied. Topics involving the application of electrochemistry to the nuclear fuel cycle, chemical sensors, energy storage, materials synthesis, refractory metals and their alloys, and alkali and alkaline earth metals are included. Also included are papers that discuss various technical, economic, and environmental issues associated with plant operations and industrial practices.
Download or read book Numerical Index of AEC Reports with Indications of Their Availability written by U.S. Atomic Energy Commission. Technical Information Service and published by . This book was released on 1951 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
