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Author: Nicolas Boumal
Publisher: Cambridge University Press
Published: 2023-03-16
Total Pages: 357
ISBN-13: 1009166174
DOWNLOAD EBOOK →An invitation to optimization with Riemannian geometry for applied mathematics, computer science and engineering students and researchers.
Author: Nicolas Boumal
Publisher: Cambridge University Press
Published: 2023-03-16
Total Pages: 358
ISBN-13: 1009178717
DOWNLOAD EBOOK →Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 646
ISBN-13: 0387217525
DOWNLOAD EBOOK →Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Author: Hiroyuki Sato
Publisher: Springer Nature
Published: 2021-02-17
Total Pages: 129
ISBN-13: 3030623912
DOWNLOAD EBOOK →This brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields. To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2000
Total Pages: 395
ISBN-13: 0387987592
DOWNLOAD EBOOK →Exercises in the text, especially in the first part of the book. Author states, that they have to be solved, without the solutions, the text is incomplete. Includes also problems after each chapter
Author: P.-A. Absil
Publisher: Princeton University Press
Published: 2009-04-11
Total Pages: 240
ISBN-13: 9781400830244
DOWNLOAD EBOOK →Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
Author: Jet Nestruev
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 226
ISBN-13: 0387227393
DOWNLOAD EBOOK →This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Author: John M. Lee
Publisher: Springer
Published: 2019-01-02
Total Pages: 437
ISBN-13: 3319917552
DOWNLOAD EBOOK →This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Author: John M. Lee
Publisher: Springer
Published: 2002-10-01
Total Pages: 628
ISBN-13: 9780387954950
DOWNLOAD EBOOK →Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Author: Yipeng Liu
Publisher: Academic Press
Published: 2021-10-21
Total Pages: 598
ISBN-13: 0323859658
DOWNLOAD EBOOK →Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application
