Sparse Grids And Applications
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Sparse Grids And Applications
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Author : Jochen Garcke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-13
Sparse Grids And Applications written by Jochen Garcke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-13 with Mathematics categories.
In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.
Sparse Grids And Applications Munich 2012
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Author : Jochen Garcke
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-11
Sparse Grids And Applications Munich 2012 written by Jochen Garcke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-11 with Mathematics categories.
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
Sparse Grids And Applications Munich 2018
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Author : Hans-Joachim Bungartz
language : en
Publisher: Springer Nature
Release Date : 2022-03-14
Sparse Grids And Applications Munich 2018 written by Hans-Joachim Bungartz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-14 with Mathematics categories.
Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.
Sparse Grids And Applications Miami 2016
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Author : Jochen Garcke
language : en
Publisher: Springer
Release Date : 2018-06-20
Sparse Grids And Applications Miami 2016 written by Jochen Garcke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Mathematics categories.
Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fourth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few.
Sparse Grids And Applications Stuttgart 2014
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Author : Jochen Garcke
language : en
Publisher: Springer
Release Date : 2016-03-16
Sparse Grids And Applications Stuttgart 2014 written by Jochen Garcke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-16 with Computers categories.
This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.
Sparse Grid Quadrature In High Dimensions With Applications In Finance And Insurance
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Author : Markus Holtz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-22
Sparse Grid Quadrature In High Dimensions With Applications In Finance And Insurance written by Markus Holtz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-22 with Mathematics categories.
This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.
Sparse Grid Methods For Higher Dimensional Approximation
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Author : Christian Feuersänger
language : en
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2010
Sparse Grid Methods For Higher Dimensional Approximation written by Christian Feuersänger and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Approximation of functions depending on more than three variables is relevant for the simulation of dynamic models. Especially stochastic models lead to a wide range of applications like simulation of polymeric liquids, kinetic equations for forces acting on offshore wind parks, or even the pricing of financial products. Sparse Grids have been designed to significantly reduce the cost to approximate high-dimensional functions under certain smoothness conditions. This book presents tools to design and work with Sparse Grids, including construction properties, algorithms, data structures and error estimates. It also discusses inherent limitations and their benefits when it comes to the simulation of stochastic models, namely to the representation of probability density functions. Furthermore, the book reveals new space- and dimension-adaptive Sparse Grids which are suitable for functions that effectively depend on only a few of their input variables.
Numerical Analysis And Its Applications
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Author : Lubin Vulkov
language : en
Publisher: Springer
Release Date : 2003-07-31
Numerical Analysis And Its Applications written by Lubin Vulkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Mathematics categories.
This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Numerical Analysis and Its Applications, NAA 2000, held in Rousse, Bulgaria in June 2000.The 90 revised papers presented were carefully selected for inclusion in the book during the two rounds of inspection and reviewing. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, etc.
Software For Exascale Computing Sppexa 2013 2015
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Author : Hans-Joachim Bungartz
language : en
Publisher: Springer
Release Date : 2016-09-14
Software For Exascale Computing Sppexa 2013 2015 written by Hans-Joachim Bungartz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Computers categories.
The research and its outcomes presented in this collection focus on various aspects of high-performance computing (HPC) software and its development which is confronted with various challenges as today's supercomputer technology heads towards exascale computing. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The collection thereby highlights pioneering research findings as well as innovative concepts in exascale software development that have been conducted under the umbrella of the priority programme "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) and that have been presented at the SPPEXA Symposium, Jan 25-27 2016, in Munich. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
Recent Trends In Computational Engineering Ce2014
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Author : Miriam Mehl
language : en
Publisher: Springer
Release Date : 2015-10-12
Recent Trends In Computational Engineering Ce2014 written by Miriam Mehl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with Computers categories.
This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer architectures, and novel mathematical approaches. Accordingly, the chapters of the book particularly focus on parallel algorithms and performance optimization, coupled systems, and complex applications and optimization.