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Dynamics of Number Systems: Computation with Arbitrary Precision 1st ed. 2016 [Kõva köide]

  • Formaat: Hardback, 224 pages, kõrgus x laius: 235x155 mm, kaal: 4794 g, 74 Illustrations, black and white; XI, 224 p. 74 illus., 1 Hardback
  • Sari: Studies in Systems, Decision and Control 59
  • Ilmumisaeg: 10-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319333666
  • ISBN-13: 9783319333663
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Dynamics of Number Systems: Computation with Arbitrary Precision 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 224 pages, kõrgus x laius: 235x155 mm, kaal: 4794 g, 74 Illustrations, black and white; XI, 224 p. 74 illus., 1 Hardback
  • Sari: Studies in Systems, Decision and Control 59
  • Ilmumisaeg: 10-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319333666
  • ISBN-13: 9783319333663
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319333663.html
Märksõnad:
This book is a source of valuable and usefulinformation on the topics of dynamics of number systems and scientificcomputation with arbitrary precision. It is addressed to scholars, scientistsand engineers, and graduate students. The treatment is elementary andself-contained with relevance both for theory and applications. The basicprerequisite of the book is linear algebra and matrix calculus.

Introduction.- Symbolic Dynamics.- Matrices and Transformations.- M obius Number Systems.- Arithmetical Algorithms.- Integer Vectors and Matrices.- Algebraic Number Fields.- Transcendent Algorithms.

Arvustused

The book is a source of valuable and useful information on dynamics of number systems and scientific computation with arbitrary precision. It is addressed to scholars, scientists and engineers, and graduate students. The treatment is elementary and self-contained with focus both to the theory and applications. (Ilia V. Boikov, zbMATH 1376.37119, 2018)

1 Introduction
1(24)
1.1 The Decadic System
1(2)
1.2 Redundancy
3(1)
1.3 Symbolic Spaces
4(1)
1.4 The Extended Real Line R
5(3)
1.5 Positional Systems for Bounded Intervals
8(4)
1.6 Positional Systems for R
12(6)
1.7 Continued Fractions
18(7)
2 Symbolic Dynamics
25(22)
2.1 Metric Spaces
25(5)
2.2 The Cantor Space
30(3)
2.3 Redundant Symbolic Extensions
33(5)
2.4 Subshifts
38(2)
2.5 Sofic Subshifts
40(3)
2.6 Labelled Graphs
43(4)
References
46(1)
3 Matrices and Transformations
47(36)
3.1 Projective Geometry
47(2)
3.2 The Extended Real Line
49(2)
3.3 Intervals
51(1)
3.4 Projective Metrics
52(2)
3.5 Transformations
54(3)
3.6 The Circle Derivation
57(1)
3.7 Conjugated Transformations
58(4)
3.8 Complex Transformations
62(2)
3.9 Hyperbolic Geometry
64(3)
3.10 Disc Transformations
67(3)
3.11 Isometric Circles
70(5)
3.12 Singular Transformations
75(2)
3.13 Representing Sequences
77(2)
3.14 General Continued Fractions
79(4)
References
81(2)
4 Mobius Number Systems
83(36)
4.1 Iterative Systems
83(4)
4.2 Interval Number Systems
87(8)
4.3 Sofic Expansion Subshifts
95(4)
4.4 Partition Number Systems
99(4)
4.5 Sofic Number Systems
103(5)
4.6 The Contraction and Length Quotients
108(3)
4.7 Polygonal Number Systems
111(3)
4.8 Discrete Groups
114(5)
References
117(2)
5 Arithmetical Algorithms
119(28)
5.1 Intervals
120(5)
5.2 The Unary Algorithm
125(3)
5.3 The Branching Unary Algorithm
128(2)
5.4 Bilinear Tensors
130(7)
5.5 The Binary Algorithm
137(4)
5.6 Polynomials
141(2)
5.7 Rational Functions
143(4)
References
145(2)
6 Integer Vectors and Matrices
147(18)
6.1 Determinant and Norm
147(3)
6.2 Rational Number Systems
150(2)
6.3 Modular Number Systems
152(3)
6.4 Finite State Transducers
155(3)
6.5 Bimodular Systems
158(4)
6.6 Binary Continued Fractions
162(3)
References
164(1)
7 Algebraic Number Fields
165(32)
7.1 Polynomials with Rational Coefficients
165(1)
7.2 Extension Fields
166(6)
7.3 Field Embeddings
172(3)
7.4 Computable Ordered Fields
175(1)
7.5 Algebraic Integers
176(3)
7.6 Pisot and Salem Numbers
179(1)
7.7 Positional Number Systems
180(8)
7.8 Arithmetic in Positional Systems
188(9)
References
195(2)
8 Transcendent Algorithms
197(24)
8.1 Pade Approximants
197(8)
8.2 Algebraic Tensors
205(4)
8.3 The Transcendent Algorithm
209(6)
8.4 Arithmetical Expressions
215(2)
8.5 Iterative Algorithms
217(4)
References
219(2)
Index 221