Sparse Polynomial Approximation Of High Dimensional Functions PDF Download
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| Author | : Ben Adcock |
| Publisher | : SIAM |
| Total Pages | : 310 |
| Release | : 2022-02-16 |
| Genre | : Mathematics |
| ISBN | : 161197688X |
Download Sparse Polynomial Approximation of High-Dimensional Functions Book in PDF, ePub and Kindle
Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
| Author | : Ben Adcock |
| Publisher | : Society for Industrial and Applied Mathematics (SIAM) |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : Approximation theory |
| ISBN | : 9781611976878 |
Download Sparse Polynomial Approximation of High-Dimensional Functions Book in PDF, ePub and Kindle
"This is a book about polynomial approximation in high dimensions"--
| Author | : Ashkan Nikeghbali |
| Publisher | : Springer Nature |
| Total Pages | : 417 |
| Release | : 2022-08-04 |
| Genre | : Mathematics |
| ISBN | : 3031008324 |
Download High-Dimensional Optimization and Probability Book in PDF, ePub and Kindle
This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 590 |
| Release | : 2024-06-13 |
| Genre | : Mathematics |
| ISBN | : 0443239851 |
Download Numerical Analysis meets Machine Learning Book in PDF, ePub and Kindle
Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on the Numerical Analysis Meets Machine Learning
| Author | : Holger Boche |
| Publisher | : Birkhäuser |
| Total Pages | : 388 |
| Release | : 2018-01-17 |
| Genre | : Mathematics |
| ISBN | : 3319698028 |
Download Compressed Sensing and its Applications Book in PDF, ePub and Kindle
This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.
| Author | : Aicke Hinrichs |
| Publisher | : Springer Nature |
| Total Pages | : 657 |
| Release | : |
| Genre | : |
| ISBN | : 3031597621 |
Download Monte Carlo and Quasi-Monte Carlo Methods Book in PDF, ePub and Kindle
| Author | : Spencer J. Sherwin |
| Publisher | : Springer Nature |
| Total Pages | : 658 |
| Release | : 2020-08-11 |
| Genre | : Mathematics |
| ISBN | : 3030396479 |
Download Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 Book in PDF, ePub and Kindle
This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
| Author | : Ben Adcock |
| Publisher | : Cambridge University Press |
| Total Pages | : 620 |
| Release | : 2021-09-16 |
| Genre | : Computers |
| ISBN | : 1108383912 |
Download Compressive Imaging: Structure, Sampling, Learning Book in PDF, ePub and Kindle
Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging – including compressed sensing, wavelets and optimization – in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the pitfalls of these latest approaches.
| Author | : Gianluigi Rozza |
| Publisher | : SIAM |
| Total Pages | : 501 |
| Release | : 2022-11-21 |
| Genre | : Mathematics |
| ISBN | : 1611977258 |
Download Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics Book in PDF, ePub and Kindle
Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.
| Author | : Leszek F. Demkowicz |
| Publisher | : SIAM |
| Total Pages | : 217 |
| Release | : 2023-09-22 |
| Genre | : Mathematics |
| ISBN | : 1611977738 |
Download Mathematical Theory of Finite Elements Book in PDF, ePub and Kindle
This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
