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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.

Computational grids (Computer systems) --- Computer science --- Computer science. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Mathematics. --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics.

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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.

Complex analysis --- Mathematics --- Computer science --- Computer. Automation --- complexe analyse (wiskunde) --- computers --- informatica --- wiskunde --- algoritmen --- informaticaonderzoek

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This book provides an introduction to mathematical and computer-oriented modeling and to simulation as a universal methodology. It therefore addresses various model classes and their derivations. And it demonstrates the diversity of approaches that can be taken: be it discrete or continuous, deterministic or stochastic. A common underlying theme throughout the book are the means in which one obtains practical simulation results from these different abstract models.   Subsequent to a brief review of the mathematical tools that are required, the concept of the simulation pipeline, "from model derivation to the simulation", is applied to 14 example scenarios from diverse fields such as "Game theory - deciding - planning", "Traffic on highways and data highways", "Dynamical systems" and "Physics in the computer".   Whether it is game theory or mathematical finance, traffic or control theory, population dynamics or chaos, or molecular dynamics, continuum mechanics or computer graphics - the reader gains insight into the world of simulation in a descriptive yet systematic way.

Mathematics. --- Computer simulation. --- Computer science --- Computer science. --- Computational Science and Engineering. --- Computational Mathematics and Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Simulation and Modeling. --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Informatics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Math --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Science --- Computer mathematics. --- Mathematical models. --- Models, Mathematical

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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.

Mathematics. --- Computer science --- Computer simulation. --- Approximation theory. --- Computer mathematics. --- Computational Mathematics and Numerical Analysis. --- Mathematics of Computing. --- Simulation and Modeling. --- Approximations and Expansions. --- Sparse grids. --- Numerical analysis --- Sparse matrices --- Spare matrix techniques --- Matrices --- Computer science. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Mathematics --- 519.63 --- Numerical grid generation (Numerical analysis) --- Coordinate generation, Numerical (Numerical analysis) --- Generation of numerical grids (Numerical analysis) --- Grid generation, Numerical (Numerical analysis) --- Mesh generation, Numerical (Numerical analysis) --- Numerical coordinate generation (Numerical analysis) --- Numerical mesh generation (Numerical analysis) --- Boundary value problems --- Differential equations, Partial --- Nets (Mathematics) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions --- Computer science—Mathematics. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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This book provides an introduction to mathematical and computer-oriented modeling and to simulation as a universal methodology. It therefore addresses various model classes and their derivations. And it demonstrates the diversity of approaches that can be taken: be it discrete or continuous, deterministic or stochastic. A common underlying theme throughout the book are the means in which one obtains practical simulation results from these different abstract models.   Subsequent to a brief review of the mathematical tools that are required, the concept of the simulation pipeline, "from model derivation to the simulation", is applied to 14 example scenarios from diverse fields such as "Game theory - deciding - planning", "Traffic on highways and data highways", "Dynamical systems" and "Physics in the computer".   Whether it is game theory or mathematical finance, traffic or control theory, population dynamics or chaos, or molecular dynamics, continuum mechanics or computer graphics - the reader gains insight into the world of simulation in a descriptive yet systematic way.

Mathematics --- Mathematics --- Planning (firm) --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- vormgeving --- computers --- informatica --- mathematische modellen --- mineralen (chemie) --- simulaties --- externe fixatie (geneeskunde --- mijnbouw --- wiskunde --- wiskunde --- informaticaonderzoek --- computerkunde