Analysis And Computation
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| Author | : Qiang Du |
| Publisher | : SIAM |
| Total Pages | : 181 |
| Release | : 2019-03-20 |
| Genre | : Science |
| ISBN | : 1611975611 |
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
| Author | : Wouter van Atteveldt |
| Publisher | : John Wiley & Sons |
| Total Pages | : 341 |
| Release | : 2022-03-10 |
| Genre | : Social Science |
| ISBN | : 111968028X |
Provides clear guidance on leveraging computational techniques to answer social science questions In disciplines such as political science, sociology, psychology, and media studies, the use of computational analysis is rapidly increasing. Statistical modeling, machine learning, and other computational techniques are revolutionizing the way electoral results are predicted, social sentiment is measured, consumer interest is evaluated, and much more. Computational Analysis of Communication teaches social science students and practitioners how computational methods can be used in a broad range of applications, providing discipline-relevant examples, clear explanations, and practical guidance. Assuming little or no background in data science or computer linguistics, this accessible textbook teaches readers how to use state-of-the art computational methods to perform data-driven analyses of social science issues. A cross-disciplinary team of authors—with expertise in both the social sciences and computer science—explains how to gather and clean data, manage textual, audio-visual, and network data, conduct statistical and quantitative analysis, and interpret, summarize, and visualize the results. Offered in a unique hybrid format that integrates print, ebook, and open-access online viewing, this innovative resource: Covers the essential skills for social sciences courses on big data, data visualization, text analysis, predictive analytics, and others Integrates theory, methods, and tools to provide unified approach to the subject Includes sample code in Python and links to actual research questions and cases from social science and communication studies Discusses ethical and normative issues relevant to privacy, data ownership, and reproducible social science Developed in partnership with the International Communication Association and by the editors of Computational Communication Research Computational Analysis of Communication is an invaluable textbook and reference for students taking computational methods courses in social sciences, and for professional social scientists looking to incorporate computational methods into their work.
| Author | : Allan Borodin |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 2005-02-17 |
| Genre | : Computers |
| ISBN | : 9780521619462 |
Contains theoretical foundations, applications, and examples of competitive analysis for online algorithms.
| Author | : Jeffery J. Leader |
| Publisher | : Addison-Wesley Longman |
| Total Pages | : 0 |
| Release | : 2004 |
| Genre | : Numerical analysis |
| ISBN | : 9780201734997 |
This text is intended for a first course in Numerical Analysis taken by students majoring in mathematics, engineering, computer science, and the sciences. This text emphasizes the mathematical ideas behind the methods and the idea of mixing methods for robustness. The optional use of MATLAB is incorporated throughout the text.
| Author | : Stefano Cagnoni |
| Publisher | : Hindawi Publishing Corporation |
| Total Pages | : 473 |
| Release | : 2008 |
| Genre | : Computer vision |
| ISBN | : 9774540018 |
| Author | : Zhong-Zhi Bai |
| Publisher | : SIAM |
| Total Pages | : 496 |
| Release | : 2021-09-09 |
| Genre | : Mathematics |
| ISBN | : 1611976634 |
This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
| Author | : Michael Oberguggenberger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 338 |
| Release | : 2011-03-19 |
| Genre | : Computers |
| ISBN | : 0857294466 |
This textbook presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations. Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book’s webpage.
| Author | : Tamal Krishna Dey |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1009103199 |
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
| Author | : John Wright |
| Publisher | : Cambridge University Press |
| Total Pages | : 718 |
| Release | : 2022-01-13 |
| Genre | : Computers |
| ISBN | : 1108805558 |
Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.
| Author | : Avi Wigderson |
| Publisher | : Princeton University Press |
| Total Pages | : 434 |
| Release | : 2019-10-29 |
| Genre | : Computers |
| ISBN | : 0691189137 |
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
