A General Theory Of Optimal Algorithms
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A General Theory Of Optimal Algorithms
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Author : Joseph Frederick Traub
language : en
Publisher:
Release Date : 1980
A General Theory Of Optimal Algorithms written by Joseph Frederick Traub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
The purpose of this monograph is to create a general framework for the study of optimal algorithms for problems that are solved approximately. For generality the setting is abstract, but we present many applications to practical problems and provide examples to illustrate concepts and major theorems. The work presented here is motivated by research in many fields. Influential have been questions, concepts, and results from complexity theory, algorithmic analysis, applied mathematics and numerical analysis, the mathematical theory of approximation (particularly the work on n-widths in the sense of Gelfand and Kolmogorov), applied approximation theory (particularly the theory of splines), as well as earlier work on optimal algorithms. But many of the questions we ask (see Overview) are new. We present a different view of algorithms and complexity and must request the reader's
Essays On The Complexity Of Continuous Problems
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Author : Erich Novak
language : en
Publisher: European Mathematical Society
Release Date : 2009
Essays On The Complexity Of Continuous Problems written by Erich Novak and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computational complexity categories.
This book contains five essays on the complexity of continuous problems, written for a wider audience. The first four essays are based on talks presented in 2008 when Henryk Wozniakowski received an honorary doctoral degree from the Friedrich Schiller University of Jena. The focus is on the introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of high-dimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of information-based complexity addressed to a general readership.
Elements Of The General Theory Of Optimal Algorithms
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Author : Ivan Vasilʹevich Sergienko
language : en
Publisher:
Release Date : 2021
Elements Of The General Theory Of Optimal Algorithms written by Ivan Vasilʹevich Sergienko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Algorithms categories.
In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing -solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.
Minimax Models In The Theory Of Numerical Methods
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Author : A. Sukharev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Minimax Models In The Theory Of Numerical Methods written by A. Sukharev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
In the Russian edition published in 1989, this book was called "Minimax Algorithms in Problems of Numerical Analysis". The new title is better related to the subject of the book and its style. The basis for every decision or inference concerning the ways to solve a given problem is the computa tion model. Thus, the computation model is the epicenter of any structure studied in the book. Algorithms are not constructed here, they are rather derived from computation models. Quality of an algorithm depends entirely on consistency of the model with the real-life problem. So, constructing a model is an art, deriving an algorithm is a science. We study only minimax or, in other words, worst-case computation models. However, one of the characteristic features of the book is a new approach to the notion of the worst-case conditions in dynamic processes. This approach leads to the concept of sequentially optimal algorithms, which play the central role in the book. In conclusion, I would like to express my gratitude to Prof. Dr. Heinz J. Skala and Dr. Sergei A. Orlovsky for encouraging translation of this book. I also greatly appreciate the highly professional job of Dr. Olga R. Chuyan who translated the book.
Elements Of The General Theory Of Optimal Algorithms
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Author : Ivan V. Sergienko
language : en
Publisher: Springer Nature
Release Date : 2022-01-11
Elements Of The General Theory Of Optimal Algorithms written by Ivan V. Sergienko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-11 with Mathematics categories.
In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.
Understanding Machine Learning
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Author : Shai Shalev-Shwartz
language : en
Publisher: Cambridge University Press
Release Date : 2014-05-19
Understanding Machine Learning written by Shai Shalev-Shwartz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Computers categories.
Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.
The Collected Papers Of Stephen Smale
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Author : Stephen Smale
language : en
Publisher: World Scientific
Release Date : 2000
The Collected Papers Of Stephen Smale written by Stephen Smale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
Collected Papers Of Stephen Smale The In 3 Volumes Volume 3
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Author : Roderick S C Wong
language : en
Publisher: World Scientific
Release Date : 2000-06-30
Collected Papers Of Stephen Smale The In 3 Volumes Volume 3 written by Roderick S C Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-30 with Mathematics categories.
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
Tractability Of Multivariate Problems Linear Information
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Author : Erich Novak
language : en
Publisher: European Mathematical Society
Release Date : 2008
Tractability Of Multivariate Problems Linear Information written by Erich Novak and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Multivariate problems occur in many applications. These problems are defined on spaces of $d$-variate functions and $d$ can be huge--in the hundreds or even in the thousands. Some high-dimensional problems can be solved efficiently to within $\varepsilon$, i.e., the cost increases polynomially in $\varepsilon^{-1}$ and $d$. However, there are many multivariate problems for which even the minimal cost increases exponentially in $d$. This exponential dependence on $d$ is called intractability or the curse of dimensionality. This is the first volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. It is devoted to tractability in the case of algorithms using linear information and develops the theory for multivariate problems in various settings: worst case, average case, randomized and probabilistic. A problem is tractable if its minimal cost is not exponential in $\varepsilon^{-1}$ and $d$. There are various notions of tractability, depending on how we measure the lack of exponential dependence. For example, a problem is polynomially tractable if its minimal cost is polynomial in $\varepsilon^{-1}$ and $d$. The study of tractability was initiated about 15 years ago. This is the first and only research monograph on this subject. Many multivariate problems suffer from the curse of dimensionality when they are defined over classical (unweighted) spaces. In this case, all variables and groups of variables play the same role, which causes the minimal cost to be exponential in $d$. But many practically important problems are solved today for huge $d$ in a reasonable time. One of the most intriguing challenges of the theory is to understand why this is possible. Multivariate problems may become weakly tractable, polynomially tractable or even strongly polynomially tractable if they are defined over weighted spaces with properly decaying weights. One of the main purposes of this book is to study weighted spaces and obtain necessary and sufficient conditions on weights for various notions of tractability. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It may be also suitable for graduate courses and seminars. The text concludes with a list of thirty open problems that can be good candidates for future tractability research.
Functional Analysis
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Author : Klaus D. Bierstedt
language : en
Publisher: CRC Press
Release Date : 1993-09-16
Functional Analysis written by Klaus D. Bierstedt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-16 with Mathematics categories.
These proceedings from the Symposium on Functional Analysis explore advances in the usually separate areas of semigroups of operators and evolution equations, geometry of Banach spaces and operator ideals, and Frechet spaces with applications in partial differential equations.