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 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.
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 Miami 2016 written by Jochen Garcke and published by Springer. This book was released on 2018-06-20 with total page 265 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 Munich 2012 written by Jochen Garcke and published by Springer Science & Business Media. This book was released on 2014-04-11 with total page 345 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 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 Sparse Grids and Applications Munich 2018 written by Hans-Joachim Bungartz and published by Springer Nature. This book was released on 2022-03-14 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 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 A Hyperspherical Adaptive Sparse Grid Method for High Dimensional Discontinuity Detection written by and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
Download or read book A Hyper spherical Adaptive Sparse grid Method for High dimensional Discontinuity Detection written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work proposes and analyzes a hyper-spherical adaptive hi- erarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the the- oretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a func- tion representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smooth- ness of the hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity anal- yses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
Download or read book Advances in Economics and Econometrics Volume 2 written by Bo Honoré and published by Cambridge University Press. This book was released on 2017-11-02 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montreal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics. The book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their fields. The second volume addresses topics such as big data, macroeconomics, financial markets, and partially identified models.
Download or read book Advances in Economics and Econometrics written by Econometric Society. World Congress and published by Cambridge University Press. This book was released on 2017 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montréal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics today. This book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their fields. The first volume includes theoretical and applied papers addressing topics such as dynamic mechanism design, agency problems, and networks"--
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 Handbook of Macroeconomics written by John B. Taylor and published by Elsevier. This book was released on 2016-12-01 with total page 1376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Macroeconomics surveys all major advances in macroeconomic scholarship since the publication of Volume 1 (1999), carefully distinguishing between empirical, theoretical, methodological, and policy issues. It courageously examines why existing models failed during the financial crisis, and also addresses well-deserved criticism head on. With contributions from the world's chief macroeconomists, its reevaluation of macroeconomic scholarship and speculation on its future constitute an investment worth making. Serves a double role as a textbook for macroeconomics courses and as a gateway for students to the latest research Acts as a one-of-a-kind resource as no major collections of macroeconomic essays have been published in the last decade
Download or read book Economic Dynamics second edition written by John Stachurski and published by MIT Press. This book was released on 2022-08-16 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a rigorous and example-driven introduction to topics in economic dynamics that emphasizes techniques for modeling dynamic systems. This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real-world problems. The material makes extensive use of programming examples to illustrate ideas, bringing to life the abstract concepts in the text. Key topics include algorithms and scientific computing, simulation, Markov models, and dynamic programming. Part I introduces fundamentals and part II covers more advanced material. This second edition has been thoroughly updated, drawing on recent research in the field. New for the second edition: “Programming-language agnostic” presentation using pseudocode. New chapter 1 covering conceptual issues concerning Markov chains such as ergodicity and stability. New focus in chapter 2 on algorithms and techniques for program design and high-performance computing. New focus on household problems rather than optimal growth in material on dynamic programming. Solutions to many exercises, code, and other resources available on a supplementary website.
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:
