General Theory of Optimal Error Algorithms and Analytic Complexity. Part B. Iterative Information Model PDF Download
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Author: J. F. Traub
Publisher:
ISBN:
Category :
Languages : en
Pages : 97
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Book Description
This is the second of a series of papers in which we construct an information based general theory of optimal error algorithms and analytic computational complexity and study applications of the general theory. In our first paper we studied a general information' model; here we study an 'iterative information' model. We give a general paradigm, based on the pre-image set of an information operator, for obtaining a lower bound on the error of any algorithm using this information. We show that the order of information provides an upper bound on the order of any algorithm using this information. This upper bound order leads to a lower bound on the complexity index.
Author: J. F. Traub
Publisher:
ISBN:
Category :
Languages : en
Pages : 97
Get Book Here
Book Description
This is the second of a series of papers in which we construct an information based general theory of optimal error algorithms and analytic computational complexity and study applications of the general theory. In our first paper we studied a general information' model; here we study an 'iterative information' model. We give a general paradigm, based on the pre-image set of an information operator, for obtaining a lower bound on the error of any algorithm using this information. We show that the order of information provides an upper bound on the order of any algorithm using this information. This upper bound order leads to a lower bound on the complexity index.
Author: J. F. Traub
Publisher:
ISBN:
Category :
Languages : en
Pages : 97
Get Book Here
Book Description
Author: J. F. Traub
Publisher:
ISBN:
Category :
Languages : en
Pages : 95
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Book Description
Author: J. F. Traub
Publisher:
ISBN:
Category :
Languages : en
Pages : 95
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Book Description
This is the first of a series of papers constructing an information based general theory of optimal errors and analytic computational complexity. Among the applications are such traditionally diverse areas as approximation, boundary-value problems, quadrature, and nonlinear equations in a finite or infinite dimensional space. Traditionally algorithms are often derived by ad hoc criteria. The information based theory rationalizes the synthesis of algorithms by showing how to construct algorithms which minimize or nearly minimize the error. For certain classes of problems it shows how to construct algorithms (linear optimal error algorithms) which enjoy essentially optimal complexity with respect to all possible algorithms. The existence of strongly non-computable problems is demonstrated. In contrast with the gap theorem of recursively computable functions it is shown that every monotonic real function is the complexity of some problem.
Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 568
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Book Description
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 1048
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Book Description
Author: Joseph Frederick Traub
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages :
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Book Description
Author: Erich Novak
Publisher: European Mathematical Society
ISBN: 9783037190692
Category : Computational complexity
Languages : en
Pages : 112
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Book Description
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.
Author: Technology Reports Centre (Great Britain)
Publisher:
ISBN:
Category :
Languages : en
Pages : 506
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Book Description
Author:
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 744
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Book Description
These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
