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Complexity and real computation /

Additional authors: Blum, Lenore.
Published by : Springer, (New York :) Physical details: xvi, 453 p. : ill. ; 24 cm. ISBN:0387982817 (hc : alk. paper). Year: 1998
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681.3.06 BLU (Browse shelf) 16236 Available 16236

Includes bibliographical references (p. [431]-445) and index.

I. Basic Development. 1. Introduction. 2. Definitions and First Properties of Computation. 3. Computation over a Ring. 4. Decision Problems and Complexity over a Ring. 5. The Class NP and NP-Complete Problems. 6. Integer Machines. 7. Algebraic Settings for the Problem [actual symbol not reproducible]. App. A.1. Basic Notions of Algebraic Geometry -- App. A.2. Additional Comments and Bibliographical Remarks -- II. Some Geometry of Numerical Algorithms. 8. Newton's Method. 9. Fundamental Theorem of Algebra: Complexity Aspects. 10. Bezout's Theorem. 11. Condition Numbers and the Loss of Precision of Linear Equations. 12. The Condition Number for Nonlinear Problems. 13. The Condition Number in P(H[subscript (d)]). 14. Complexity and the Condition Number. 15. Linear Programming. App. B.1. The Main Theorem of Elimination Theory -- App. B.2. Additional Comments and Bibliographical Remarks -- III. Complexity Classes over the Reals. 16. Deterministic Lower Bounds.

17. Probabilistic Machines. 18. Parallel Computations. 19. Some Separations of Complexity Classes. 20. Weak Machines. 21. Additive Machines. 22. Nonuniform Complexity Classes. 23. Descriptive Complexity.

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