Sparse Polynomial Approximation of High-Dimensional Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sparse Polynomial Approximation of High-Dimensional Functions write by Ben Adcock . This book was released on 2022-02-16. Sparse Polynomial Approximation of High-Dimensional Functions available 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.
Sparse Polynomial Approximation of High-Dimensional Functions
Sparse Polynomial Approximation of High-Dimensional Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sparse Polynomial Approximation of High-Dimensional Functions write by Ben Adcock. This book was released on 2021. Sparse Polynomial Approximation of High-Dimensional Functions available in PDF, EPUB and Kindle. "This is a book about polynomial approximation in high dimensions"--
High-Dimensional Optimization and Probability
High-Dimensional Optimization and Probability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-Dimensional Optimization and Probability write by Ashkan Nikeghbali. This book was released on 2022-08-04. High-Dimensional Optimization and Probability available 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.
Numerical Analysis meets Machine Learning
Numerical Analysis meets Machine Learning - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Analysis meets Machine Learning write by . This book was released on 2024-06-13. Numerical Analysis meets Machine Learning available 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
Compressive Imaging: Structure, Sampling, Learning
Compressive Imaging: Structure, Sampling, Learning - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Compressive Imaging: Structure, Sampling, Learning write by Ben Adcock. This book was released on 2021-09-16. Compressive Imaging: Structure, Sampling, Learning available 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.
