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Computable Analysis

An Introduction

Computable Analysis - Weihrauch, Klaus - ISBN: 9783540668176
Prijs: € 85,95
Levertijd: 4 tot 6 werkdagen
Bindwijze: Boek, Gebonden
Genre: Informatiekunde
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Merging Fundamental Concepts Of Analysis And Recursion Theory To A New Exciting Theory, This Book Provides A Solid Fundament For Studying Various Aspects Of Computability And Complexity In Analysis.


Titel: Computable Analysis
auteur: Weihrauch, Klaus
Mediatype: Boek
Bindwijze: Gebonden
Taal: Engels
Aantal pagina's: 288
Uitgever: Springer-verlag Berlin And Heidelberg Gmbh & Co. Kg
Plaats van publicatie: DE
NUR: Informatiekunde
Collectie: Texts in Theoretical Computer Science, An EATCS Series
Afmetingen: 164 x 240 x 26
Gewicht: 620 gr
ISBN/ISBN13: 3540668179
ISBN/ISBN13: 9783540668176
Intern nummer: 1154876

Biografie (woord)

Klaus Weihrauch ist seit 1990 bei der SAP AG und dort im Umfeld der Lösung Produktionsplanung und -steuerung (PP) tätig. Unter anderem erstellte er das Daten- und Prozessmodell für die R/3-Komponente PP und war im Rahmen von AcceleratedSAP für den Bereich der Produktionsplanung verantwortlich. Zurzeit ist Klaus Weihrauch Projektleiter im Bereich Best Practices for mySAP SCM, in dem vorkonfigurierte Lösungen für das Supply Chain Management erstellt werden.

Extra informatie

Is the exponential function computable? Are union and intersection of closed sets in the real plain computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for many years and is written in a style suitable for graduate-level and senior students in computer science or mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.


1. Introduction.- 1.1 The Aim of Computable Analysis.- 1.2 Why a New Introduction?.- 1.3 A Sketch of TTE.- 1.3.1 A Model of Computation.- 1.3.2 A Naming System for Real Numbers.- 1.3.3 Computable Real Numbers and Functions.- 1.3.4 Subsets of Real Numbers.- 1.3.5 The Space C[O;1] of ContinuouS Functions.- 1.3.6 Computational Complexity of Real Functions.- 1.4 Prerequisites aud Notation.- 2. Computability on the Cantor Space.- 2.1 Type-2 Machines and Computable String Functions.- 2.2 Computable String Functions are Continuous.- 2.3 Standard Representations of Sets of Continuous String Functions.- 2.4 Effective Subsets.- 3. Naming Systems.- 3.1 Continuity and Computability Induced by Naming Systems.- 3.2 Admissible Naming Systems.- 3.3 Constructions of New Naming Systems.- 4. Computability on the Real Numbers.- 4.1 Various Representations of the Real Numbers.- 4.2 Computable Real Numbers.- 4.3 Computable Real Functions.- 5. Computability on Closed, Open and Compact Sets.- 5.1 Closed Sets and Open Sets.- 5.2 Compact Sets.- 6. Spaces of Continuous Functions.- 6.1 Various representations.- 6.2 Computable Operators on Functions. Sets and Numbers.- 6.3 Zero-Finding.- 6.4 Differentiation and Integration.- 6.5 Analytic Functions.- 7. Computational Complexity.- 7.1 Complexity of Type-2 Machine Computations.- 7.2 Complexity Induced by the Signed Digit Representation.- 7.3 The Complexity of Some Real Functions.- 7.4 Complexity on Compact Sets.- 8. Some Extensions.- 8.1 Computable Metric Spaces.- 8.2 Degrees of Discontinuity.- 9. Other Approaches to Computable Analysis.- 9.1 Banach/Mazur Computability.- 9.2 Grzegorczyk's Characterizations.- 9.3 The Pour-El/Richards Approach.- 9.4 Ko's Approach.- 9.5 Domain Theory.- 9.6 Markov's Approach.- 9.7 The real-RAM and Related Models.- 9.8 Comparison.- References.


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