Information-based Complexity - 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 Information-based Complexity write by Joseph Frederick Traub. This book was released on 1988. Information-based Complexity available in PDF, EPUB and Kindle. This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems for which the information is partial, noisy, and priced. Such problems arise in many areas including economics, physics, human and robotic vision, scientific and engineering computation, geophysics, decision theory, signal processing and control theory.
Complexity and Information
Complexity and Information - 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 Complexity and Information write by J. F. Traub. This book was released on 1998-12-10. Complexity and Information available in PDF, EPUB and Kindle. The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.
Multivariate Algorithms and Information-Based Complexity
Multivariate Algorithms and Information-Based Complexity - 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 Multivariate Algorithms and Information-Based Complexity write by Fred J. Hickernell. This book was released on 2020-06-08. Multivariate Algorithms and Information-Based Complexity available in PDF, EPUB and Kindle. The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.
An Introduction to Kolmogorov Complexity and Its Applications
An Introduction to Kolmogorov Complexity and Its Applications - 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 An Introduction to Kolmogorov Complexity and Its Applications write by Ming Li. This book was released on 2013-03-09. An Introduction to Kolmogorov Complexity and Its Applications available in PDF, EPUB and Kindle. Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Information and Complexity in Statistical Modeling
Information and Complexity in Statistical Modeling - 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 Information and Complexity in Statistical Modeling write by Jorma Rissanen. This book was released on 2007-12-15. Information and Complexity in Statistical Modeling available in PDF, EPUB and Kindle. No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
