Computable Analysis
Springer Berlin (Verlag)
978-3-540-66817-6 (ISBN)
Klaus Weihrauch ist Professor an der Fernuniversitaet in Hagen.
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.
Erscheint lt. Verlag | 14.9.2000 |
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Reihe/Serie | Texts in Theoretical Computer Science. An EATCS Series |
Verlagsort | Berlin |
Sprache | englisch |
Gewicht | 568 g |
Einbandart | gebunden |
Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
Mathematik / Informatik ► Mathematik ► Analysis | |
Schlagworte | Algorithm analysis and problem complexity • Analysis • Analysis; Handbuch/Lehrbuch (Informatik) • Complexity • complexity in analysis • Computability • computability in analysis • computable analysis • computable real functions • Computer • Computer Science |
ISBN-10 | 3-540-66817-9 / 3540668179 |
ISBN-13 | 978-3-540-66817-6 / 9783540668176 |
Zustand | Neuware |
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