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This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.
Mathematics. --- Computer science --- Approximations and Expansions. --- Computational Mathematics and Numerical Analysis. --- Signal, Image and Speech Processing. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Mathematics --- Approximation theory. --- Computer mathematics. --- Signal processing. --- Image processing. --- Speech processing systems. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)
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This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.
Mathematics --- Computer science --- Computer. Automation --- beeldverwerking --- spraaktechnologie --- informatica --- externe fixatie (geneeskunde --- wiskunde --- gegevensanalyse --- signaalverwerking
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Hydrocarbon exploration and production incorporate great technology challenges for the oil and gas industry. In order to meet the world's future demand for oil and gas, further technological advance is needed, which in turn requires research across multiple disciplines, including mathematics, geophysics, geology, petroleum engineering, signal processing, and computer science. This book addresses important aspects and fundamental concepts in hydrocarbon exploration and production. Moreover, new developments and recent advances in the relevant research areas are discussed, whereby special emphasis is placed on mathematical methods and modelling. The book reflects the multi-disciplinary character of the hydrocarbon production workflow, ranging from seismic data imaging, seismic analysis and interpretation and geological model building, to numerical reservoir simulation. Various challenges concerning the production workflow are discussed in detail. The thirteen chapters of this joint work, authored by international experts from academic and industrial institutions, include survey papers of expository character as well as original research articles. Large parts of the material presented in this book were developed between November 2000 and April 2004 through the European research and training network NetAGES, "Network for Automated Geometry Extraction from Seismic". The new methods described here are currently being implemented as software tools at Schlumberger Stavanger Research, one of the world's largest service providers to the oil industry.
Petroleum --- Petroleum mining --- Prospecting --- Mathematical models. --- Oil fields --- Coal-oil --- Crude oil --- Oil --- Caustobioliths --- Mineral oils --- Production methods --- Computer science --- Chemistry. --- Geography. --- Computer vision. --- Engineering mathematics. --- Computational Mathematics and Numerical Analysis. --- Computer Applications in Chemistry. --- Earth Sciences, general. --- Image Processing and Computer Vision. --- Theoretical, Mathematical and Computational Physics. --- Mathematical and Computational Engineering. --- Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Cosmography --- Earth sciences --- World history --- Physical sciences --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics. --- Chemoinformatics. --- Earth sciences. --- Optical data processing. --- Mathematical physics. --- Applied mathematics. --- Physical mathematics --- Physics --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Geosciences --- Environmental sciences --- Chemical informatics --- Chemiinformatics --- Chemoinformatics --- Chemistry informatics --- Chemistry --- Information science --- Computational chemistry --- Optical equipment --- Data processing
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This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.
Computer science. --- Oceanography. --- Environmental sciences. --- Computational Science and Engineering. --- Mathematical Applications in the Physical Sciences. --- Atmospheric Sciences. --- Math. Appl. in Environmental Science. --- Environmental science --- Science --- Oceanography, Physical --- Oceanology --- Physical oceanography --- Thalassography --- Earth sciences --- Marine sciences --- Ocean --- Informatics --- Computer mathematics. --- Mathematical physics. --- Atmospheric sciences. --- Atmospheric sciences --- Atmosphere --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing --- Mathematics
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Mathematics --- Mathematical physics --- Chemistry --- Geology. Earth sciences --- Engineering sciences. Technology --- Computer. Automation --- DIP (documentimage processing) --- beeldverwerking --- analyse (wiskunde) --- chemie --- informatica --- wiskunde --- geografie --- ingenieurswetenschappen --- fysica
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Mathematics --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- analyse (wiskunde) --- functies (wiskunde) --- informatica --- wiskunde --- ingenieurswetenschappen
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This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.
Mathematics --- Hydrosphere --- Meteorology. Climatology --- General ecology and biosociology --- Environmental protection. Environmental technology --- Computer science --- atmosfeerchemie --- atmosfeerfysica --- metrologie --- milieukunde --- computers --- informatica --- wiskunde --- informaticaonderzoek --- milieutechnologie --- computerkunde --- oceanografie --- atmosfeer
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This book describes recent collaborations combining the expertise of applied mathematicians, engineers and geophysicists within a research training group (RTG) on "Modeling, Simulation and Optimization of Fluid Dynamic Applications”, funded by the Deutsche Forschungsgemeinschaft (DFG). The focus is on mathematical modeling, adaptive discretization, approximation strategies and shape optimization with PDEs. The balanced research program is based on the guiding principle that mathematics drives applications and is inspired by applications. With this leitmotif the RTG advances research in Modeling, Simulation and Optimization by an interdisciplinary approach, i.e., to stimulate fundamental education and research by highly complex applications and at the simultaneously transfer tailored mathematical methods to applied sciences. The reported research involves nine projects and addresses challenging fluid dynamic problems inspired by applied sciences, such as climate research & meteorology, energy, aerospace & marine engineering, or medicine. More fundamental research concerning analysis, approximation and numerics is also covered. The material represents a successful attempt to exchange research paradigms between different disciplines and thus displays a modern approach to basic research into scientifically and societally relevant contemporary problems.
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Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.
Mathematics --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- analyse (wiskunde) --- functies (wiskunde) --- informatica --- wiskunde --- ingenieurswetenschappen
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