Operator Adapted Wavelets Fast Solvers And Numerical Homogenization
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Operator Adapted Wavelets Fast Solvers And Numerical Homogenization
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Author : Houman Owhadi
language : en
Publisher: Cambridge University Press
Release Date : 2019-10-24
Operator Adapted Wavelets Fast Solvers And Numerical Homogenization written by Houman Owhadi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-24 with Mathematics categories.
Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.
Numerical Homogenization By Localized Decomposition
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Author : Axel Målqvist
language : en
Publisher: SIAM
Release Date : 2020-11-23
Numerical Homogenization By Localized Decomposition written by Axel Målqvist and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Mathematics categories.
This book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems. Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
Quasi Interpolation
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Author : Martin Dietrich Buhmann
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-03
Quasi Interpolation written by Martin Dietrich Buhmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Computers categories.
Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.
Spaces Of Measures And Their Applications To Structured Population Models
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Author : Christian Düll
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-07
Spaces Of Measures And Their Applications To Structured Population Models written by Christian Düll and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-07 with Business & Economics categories.
Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.
Discrete Variational Problems With Interfaces
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Author : Roberto Alicandro
language : en
Publisher: Cambridge University Press
Release Date : 2023-12-21
Discrete Variational Problems With Interfaces written by Roberto Alicandro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-21 with Mathematics categories.
Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
Geometry Of The Phase Retrieval Problem
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Author : Alexander H. Barnett
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-05
Geometry Of The Phase Retrieval Problem written by Alexander H. Barnett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Mathematics categories.
This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.
The Christoffel Darboux Kernel For Data Analysis
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Author : Jean Bernard Lasserre
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-07
The Christoffel Darboux Kernel For Data Analysis written by Jean Bernard Lasserre and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-07 with Computers categories.
This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.
Kernel Mode Decomposition And The Programming Of Kernels
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Author : Houman Owhadi
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Kernel Mode Decomposition And The Programming Of Kernels written by Houman Owhadi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework. Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes. It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.
Explorations In The Mathematics Of Data Science
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Author : Simon Foucart
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
Explorations In The Mathematics Of Data Science written by Simon Foucart and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
This edited volume reports on the recent activities of the new Center for Approximation and Mathematical Data Analytics (CAMDA) at Texas A&M University. Chapters are based on talks from CAMDA’s inaugural conference – held in May 2023 – and its seminar series, as well as work performed by members of the Center. They showcase the interdisciplinary nature of data science, emphasizing its mathematical and theoretical foundations, especially those rooted in approximation theory.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.