Download or read book Sparse Grids and Applications Miami 2016 written by Jochen Garcke and published by Springer. This book was released on 2019-02-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparse Grids and Applications written by Jochen Garcke and published by Springer. This book was released on 2014-11-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spatially Adaptive Sparse Grids for High dimensional Problems written by Dirk Pflüger and published by . This book was released on 2010 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sparse Grids and Applications Munich 2018 written by Hans-Joachim Bungartz and published by Springer. This book was released on 2022-04-21 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparse Grids and Applications Munich 2012 written by Jochen Garcke and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Using Adaptive Sparse Grids to Solve High Dimensional Dynamic Models written by Johannes Brumm and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a flexible and scalable method for computing global solutions of high-dimensional stochastic dynamic models. Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance in regions with steep gradients or at non-differentiabilities. To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high-performance computing architectures. To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high-dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu-cost models with temporary sales and economies of scope in price setting.
Download or read book Sparse Grids and Applications Stuttgart 2014 written by Jochen Garcke and published by Springer. This book was released on 2016-03-16 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparse Grid Methods for Higher Dimensional Approximation written by Christian Feuersänger and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2010 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Subspace optimal Data Mining on Spatially Adaptive Sparse Grids written by Maximilian Luz and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extending Adaptive Sparse Grids for Stochastic Collocation to Hybrid Parallel Architectures written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We are developing an adaptive sparse grid library tailored for emerging architectures that will allow the solution of stochastic problems of unprecedented size. This paper gives a brief overview of the problem at hand and presents initial results for a small GPU-based cluster. An outlook on large-scale distributed memory parallelization and our hybrid design approach is also included.
Download or read book Transformed Sparse Grids for High dimensional Models written by Christopher Schnick and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hierarchy Direction Selective Approach for Locally Adaptive Sparse Grids written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of multidimensional adaptive hierarchical interpolation. We use sparse grids points and functions that are induced from a one dimensional hierarchical rule via tensor products. The classical locally adaptive sparse grid algorithm uses an isotropic refinement from the coarser to the denser levels of the hierarchy. However, the multidimensional hierarchy provides a more complex structure that allows for various anisotropic and hierarchy selective refinement techniques. We consider the more advanced refinement techniques and apply them to a number of simple test functions chosen to demonstrate the various advantages and disadvantages of each method. While there is no refinement scheme that is optimal for all functions, the fully adaptive family-direction-selective technique is usually more stable and requires fewer samples.
Download or read book Adaptive Sparse Grid Combination Solutions for a Singular Perturbation Problem written by J. Noordmans and published by . This book was released on 1999 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Sparse Grid Based Generative Topographic Mapping for the Dimensionality Reduction of High dimensional Data written by Michael Griebel and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Most high-dimensional data exhibit some correlation such that data points are not distributed uniformly in the data space but lie approximately on a lower-dimensional manifold. A major problem in many data-mining applications is the detection of such a manifold from given data, if present at all. The generative topographic mapping (GTM) finds a lower-dimensional parameterization for the data and thus allows for non-linear dimensionality reduction. We will show how a discretization based on sparse grids can be employed for the mapping between latent space and data space. This leads to efficient computations and avoids the 'curse of dimensionality' of the embedding dimension. We will use our modified, sparse grid based GTM for problems from dimensionality reduction and data classification.
Download or read book Sparse Grids and Related Approximation Schemes for Higher Dimensional Problems written by Michael Griebel and published by . This book was released on 2005 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sparse Grids and Applications Munich 2018 written by and published by . This book was released on 2021 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparse Grids and Applications written by Jochen Garcke and published by Springer Science & Business Media. This book was released on 2012-10-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
