Algebraic complexity theory
This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and offering over 350 exercises, it is well-suited as a textbook for beginners at graduate level. With its...
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| Other Authors: | , |
| Format: | Book |
| Language: | English |
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Berlin, Germany
Springer
1997
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| Series: | Grundlehren der mathematischen Wissenschaften
315 |
| Subjects: | |
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| 040 | |a UPNM | ||
| 090 | |a QA 267.7 |b .B87 1997 | ||
| 100 | 1 | |a Burgisser, Peter | |
| 245 | 1 | 0 | |a Algebraic complexity theory |c Peter Burgisser, Michael Clausen, M. Amin Shokrollahi ; with the collaboration of Thomas Lickteig |
| 260 | |a Berlin, Germany |b Springer |c 1997 | ||
| 300 | |a xxiii, 618 p. |b ill. |c 24 cm. | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |x 0072-7830 |v 315 | |
| 505 | |a Ch. 1. Introduction -- Ch. 2. Efficient Polynomial Arithmetic -- Ch. 3. Efficient Algorithms with Branching -- Ch. 4. Models of Computation -- Ch. 5. Preconditioning and Transcendence Degree -- Ch. 6. The Substitution Method -- Ch. 7. Differential Methods -- Ch. 8. The Degree Bound -- Ch. 9. Specific Polynomials which Are Hard to Compute -- Ch. 10. Branching and Degree -- Ch. 11. Branching and Connectivity -- Ch. 12. Additive Complexity -- Ch. 13. Linear Complexity -- Ch. 14. Multiplicative and Bilinear Complexity -- Ch. 15. Asymptotic Complexity of Matrix Multiplication -- Ch. 16. Problems Related to Matrix Multiplication -- Ch. 17. Lower Bounds for the Complexity of Algebras -- Ch. 18. Rank over Finite Fields and Codes -- Ch. 19. Rank of 2-Slice and 3-Slice Tensors -- Ch. 20. Typical Tensorial Rank -- Ch. 21. P Versus NP: A Nonuniform Algebraic Analogue. | ||
| 520 | |a This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and offering over 350 exercises, it is well-suited as a textbook for beginners at graduate level. With its extensive bibliography covering about 500 research papers, this text is also an ideal reference book for the professional researcher. The subdivision of the contents into 21 more or less independent chapters enables readers to familiarize themselves quickly with a specific topic, and facilitates the use of this book as a basis for complementary courses in other areas such as computer algebra. | ||
| 650 | 0 | |a Computational complexity | |
| 700 | 1 | |a Clausen, Michael | |
| 700 | 1 | |a Shokrollahi, Mohammad Amin | |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften |v 315 | |
| 999 | |a vtls000051374 |c 48505 |d 48505 | ||