国外数学名著系列代数复杂性理论影印版

内容简介

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《代数复杂性理论(影印版)》的作者诺维科夫是俄罗斯科学院的院士,曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到**好的指导作用。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点,基础数学类的书以“经典”为主,应用和计算数学类的书“前沿”为主。

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目录

Chapter 1.Introduction1.1 Exercises1.2 Open Problems1.3 NotesPartⅠ.Fundamental AlgorithmsChapter 2. Efficient Polynomial Arithmetic2.1 Multiplication of Polynomials I2.2* Multiplication of Polynomials II2.3* Multiplication of Several Polynomials2.4 Multiplication and Inversion of Power Series2.5* Composition of Power Series2.6 Exercises2.7 Open Problems2.8 NotesChapter 3. Efficient Algorithms with Branching3.1 Polynomial Greatest Common Divisors3.2* Local Analysis of the Knuth-Schonhage Algorithm3.3 Evaluation and Interpolation3.4* Fast Point Location in Arrangements of Hyperplanes3.5* Vapnik-Chervonenkis Dimension and Epsilon-Nets3.6 Exercises3.7 Open Problems3.8 NotesPartⅡ.Elementary Lower BoundsChapter 4. Models of Computation4.1 Straight-Line Programs and Complexity4.2 Computation Sequences4.3* Autarky4.4* Computation Trees4.5* Computation Trees and Straight-line Programs4.6 Exercises4.7 NotesChapter 5. Preconditioning and Transcendence Degree5.1 Preconditioning5.2 Transcendence Degree5.3* Extension to Linearly Disjoint Fields5.4 Exercises5.5 Open Problems5.6 NotesChapter 6. The Substitution Method6.1 Discussion of Ideas6.2 Lower Bounds by the Degree of Linearization6.3* Continued Fractions, Quotients, and Composition6.4 Exercises6.5 Open Problems6.6 NotesChapter 7. Differential Methods7.1 Complexity of Truncated Taylor Series7.2 Complexity of Partial Derivatives7.3 Exercises7.4 Open Problems7.5 NotesPart Ⅲ.High DegreeChapter 8. The Degree Bound8.1 A Field Theoretic Version of the Degree Bound8.2 Geometric Degree and a Bezout Inequality8.3 The Degree Bound8.4 Applications8.5* Estimates for the Degree8.6* The Case of a Finite Field8.7 Exercises8.8 Open Problems8.9 NotesChapter 9. Specific Polynomials which Are Hard to Compute9.1 A Genetic Computation9.2 Polynomials with Algebraic Coefficients9.3 Applications9.4* Polynomials with Rapidly Growing Integer Coefficients9.5* Extension to other Complexity Measures9.6 Exercises9.7 Open Problems9.8 NotesChapter 10. Branching and Degree10.1 Computation Trees and the Degree Bound10.2 Complexity of the Euclidean Representation10.3* Degree Pattern of the Euclidean Representation10.4 Exercises10.5 Open Problems10.6 NotesChapter 11. Branching and Connectivity11.1 Estimation of the Number of Connected Component11.2 Lower Bounds by the Number of Connected Components11.3 Knapsack and Applications to Computational Geometry11.4 Exercises11.5 Open Problems11.6 NotesChapter 12. Additive Complexity12.1 Introduction12.2* Real Roots of Sparse Systems of Equations12.3 A Bound on the Additive Complexity12.4 Exercises12.5 Open Problems12.6 NotesPart Ⅳ.Low DegreeChapter 13. Linear Complexity13.1 The Linear Computational Model13.2 First Upper and Lower Bounds13.3* A Graph Theoretical Approach13.4* Lower Bounds via Graph Theoretical Methods13.5* Generalized Fourier Transforms13.6 Exercises13.7 Open Problems13.8 NotesChapter 14. Multiplicative and Bilinear Complexity14.1 Multiplicative Complexity of Quadratic Maps14.2 The Tensorial Notation14.3 Restriction and Conciseness14.4 Other Characterizations of Rank14.5 Rank of the Polynomial Multiplication14.6 The Semiring T14.7 Exercises14.8 Open Problems14.9 Notes……Chapter 15. Asymptotic Complexity of Matrix MultiplicationChapter 16. Problems Related to Matrix MultiplicationChapter 17. Lower Bounds for the Complexity of AlgebrasChapter 18. Rank over Finite Fields and CodesChapter 19. Rank of 2-Slice and 3-Slice TensorsChapter 20. Typical Tensorial RankPart Ⅴ.Complete ProblemsChapter 21. P Versus NP:A Nonuniform Algebraic AnalogueBibliographyList of NotationIndex

封面

国外数学名著系列代数复杂性理论影印版

书名:国外数学名著系列代数复杂性理论影印版

作者:(瑞士)比尔吉斯尔(Peter Burg

页数:618

定价:¥198.0

出版社:科学出版社

出版日期:2007-01-01

ISBN:9787030182999

PDF电子书大小:120MB 高清扫描完整版

百度云下载:http://www.chendianrong.com/703018299.html

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