Sketching as a Tool for Numerical Linear Algebra highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compressed it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. It is an ideal primer for researchers and students of theoretical computer science interested in how sketching techniques can be used to speed up numerical linear algebra applications.
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Modern day cellular mobile networks use Massive MIMO technology to extend range and service multiple devices within a cell. This has brought tremendous improvements in the high peak data rates that can be handled. Nevertheless, one of the characteristics of this technology is large variations in the quality of service dependent on where the end user is located in any given cell. This becomes increasingly problematic when we are creating a society where wireless access is supposed to be ubiquitous. When payments, navigation, entertainment, and control of autonomous vehicles are all relying on wireless connectivity the primary goal for future mobile networks should not be to increase the peak rates, but the rates that can be guaranteed to the vast majority of the locations in the geographical coverage area. The cellular network architecture was not designed for high-rate data services but for low-rate voice services, thus it is time to look beyond the cellular paradigm and make a clean-slate network design that can reach the performance requirements of the future. This monograph considers the cell-free network architecture that is designed to reach the aforementioned goal of uniformly high data rates everywhere. The authors introduce the concept of a cell-free network before laying out the foundations of what is required to design and build such a network. They cover the foundations of channel estimation, signal processing, pilot assignment, dynamic cooperation cluster formation, power optimization, fronthaul signaling, and spectral efficiency evaluation in uplink and downlink under different degrees of cooperation among the access points and arbitrary linear combining and precoding. This monograph provides the reader with all the fundamental information required to design and build the next generation mobile networks without being hindered by the inherent restrictions of modern cellular-based technology.
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Randomized Algorithms for Matrices and Data provides a detailed overview, appropriate for both students and researchers from all of these areas, of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis
This book constitutes the proceedings of the 14th International Computer Science Symposium in Russia, CSR 2019, held in Novosibirsk, Russia, in July 2019. The 31 full papers were carefully reviewed and selected from 71 submissions. The papers cover a wide range of topics such as algorithms and data structures; computational complexity; randomness in computing; approximation algorithms; combinatorial optimization; constraint satisfaction; computational geometry; formal languages and automata; codes and cryptography; combinatorics in computer science; applications of logic to computer science; proof complexity; fundamentals of machine learning; and theoretical aspects of big data.
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
