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Book Freeshipping Algebraic Complexity Theory, By Peter Burgisser Etc, English, Hardcover, 2007

Posted at: Offers to Sell and Export | Posted on: Fri 21 May, 2010 8:54 am | Product Category: Algebra or pre algebra reference guides [21]
book freeshipping algebraic complexity theory peter burgisser english hardcover 2007
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Algebraic Complexity Theory, by Peter Burgisser etc, English, Hardcover, 2007

Product Details


Peter Burgisser etc

Press Science Press

Isbn 9787030182999

Publication Date Jan 2007

Pages 618

Size 16K

Edition First

Cover Hardcover

Language English

Page material gelatine plate paper

Product Description:

Science Press imported 23 books about math from Springer Press for the purpose of building a better academia; this one is one of them.


Chapter 1.Introduction

 1.1 Exercises

 1.2 Open Problems

 1.3 Notes

PartⅠ.Fundamental Algorithms

 Chapter 2. Efficient Polynomial Arithmetic

  2.1 Multiplication of Polynomials I

  2.2* Multiplication of Polynomials II

  2.3* Multiplication of Several Polynomials

  2.4 Multiplication and Inversion of Power Series

  2.5* Composition of Power Series

  2.6 Exercises

  2.7 Open Problems

  2.8 Notes

 Chapter 3. Efficient Algorithms with Branching

  3.1 Polynomial Greatest Common Divisors

  3.2* Local Analysis of the Knuth-Schonhage Algorithm

3.3 Evaluation and Interpolation

3.4* Fast Point Location in Arrangements of Hyperplanes

3.5* Vapnik-Chervonenkis Dimension and Epsilon-Nets

  3.6 Exercises

  3.7 Open Problems

  3.8 Notes

PartⅡ.Elementary Lower Bounds

 Chapter 4. Models of Computation

  4.1 Straight-Line Programs and Complexity

  4.2 Computation Sequences

  4.3* Autarky

  4.4* Computation Trees

  4.5* Computation Trees and Straight-line Programs

  4.6 Exercises

  4.7 Notes

 Chapter 5. Preconditioning and Transcendence Degree

  5.1 Preconditioning

  5.2 Transcendence Degree

  5.3* Extension to Linearly Disjoint Fields

  5.4 Exercises

  5.5 Open Problems

  5.6 Notes

 Chapter 6. The Substitution Method

  6.1 Discussion of Ideas

  6.2 Lower Bounds by the Degree of Linearization

  6.3* Continued Fractions, Quotients, and Composition

  6.4 Exercises

  6.5 Open Problems

  6.6 Notes

 Chapter 7. Differential Methods

  7.1 Complexity of Truncated Taylor Series

  7.2 Complexity of Partial Derivatives

  7.3 Exercises

  7.4 Open Problems

  7.5 Notes

Part Ⅲ.High Degree

 Chapter 8. The Degree Bound

  8.1 A Field Theoretic Version of the Degree Bound

  8.2 Geometric Degree and a Bezout Inequality

  8.3 The Degree Bound

  8.4 Applications

  8.5* Estimates for the Degree

  8.6* The Case of a Finite Field

  8.7 Exercises

  8.8 Open Problems

  8.9 Notes

 Chapter 9. Specific Polynomials which Are Hard to Compute

  9.1 A Genetic Computation

  9.2 Polynomials with Algebraic Coefficients

  9.3 Applications

  9.4* Polynomials with Rapidly Growing Integer Coefficients

  9.5* Extension to other Complexity Measures

  9.6 Exercises

  9.7 Open Problems

  9.8 Notes

 Chapter 10. Branching and Degree

  10.1 Computation Trees and the Degree Bound

  10.2 Complexity of the Euclidean Representation

  10.3* Degree Pattern of the Euclidean Representation

  10.4 Exercises

  10.5 Open Problems

  10.6 Notes

 Chapter 11. Branching and Connectivity

  11.1 Estimation of the Number of Connected Component 

  11.2 Lower Bounds by the Number of Connected Components

  11.3 Knapsack and Applications to Computational Geometry

  11.4 Exercises

  11.5 Open Problems

  11.6 Notes

 Chapter 12. Additive Complexity

  12.1 Introduction

  12.2* Real Roots of Sparse Systems of Equations

  12.3 A Bound on the Additive Complexity

  12.4 Exercises

  12.5 Open Problems

  12.6 Notes

Part Ⅳ.Low Degree

 Chapter 13. Linear Complexity

  13.1 The Linear Computational Model

  13.2 First Upper and Lower Bounds

  13.3* A Graph Theoretical Approach

  13.4* Lower Bounds via Graph Theoretical Methods

  13.5* Generalized Fourier Transforms

  13.6 Exercises

  13.7 Open Problems

  13.8 Notes

 Chapter 14. Multiplicative and Bilinear Complexity

  14.1 Multiplicative Complexity of Quadratic Maps

  14.2 The Tensorial Notation

  14.3 Restriction and Conciseness

  14.4 Other Characterizations of Rank

  14.5 Rank of the Polynomial Multiplication

  14.6 The Semiring T

  14.7 Exercises

  14.8 Open Problems

  14.9 Notes

 Chapter 15. Asymptotic Complexity of Matrix Multiplication

Chapter 16. Problems Related to Matrix Multiplication

Chapter 17. Lower Bounds for the Complexity of Algebras

Chapter 18. Rank over Finite Fields and Codes

Chapter 19. Rank of 2-Slice and 3-Slice Tensors

Chapter 20. Typical Tensorial Rank

Part Ⅴ.Complete Problems

 Chapter 21. P Versus NP:A Nonuniform Algebraic Analogue


List of Notation


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