Book 1998

Complexity and Real Computation

Authors:

ISBN: 978-1-4612-6873-4 (Print) 978-1-4612-0701-6 (Online)

Table of contents (23 chapters)

previous Page of 2
  1. Front Matter

    Pages i-xvi

  2. Basic Development

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-36

      Introduction

    3. No Access

      Chapter

      Pages 37-68

      Definitions and First Properties of Computation

    4. No Access

      Chapter

      Pages 69-81

      Computation over a Ring

    5. No Access

      Chapter

      Pages 83-98

      Decision Problems and Complexity over a Ring

    6. No Access

      Chapter

      Pages 99-112

      The Class NP and NP-Complete Problems

    7. No Access

      Chapter

      Pages 113-124

      Integer Machines

    8. No Access

      Chapter

      Pages 125-146

      Algebraic Settings for the Problem “P ≠ NP?”

    9. Back Matter

      Pages 147-149

  3. Some Geometry of Numerical Algorithms

    1. Front Matter

      Pages 151-151

    2. No Access

      Chapter

      Pages 153-168

      Newton’s Method

    3. No Access

      Chapter

      Pages 169-186

      Fundamental Theorem of Algebra: Complexity Aspects

    4. No Access

      Chapter

      Pages 187-200

      Bézout’s Theorem

    5. No Access

      Chapter

      Pages 201-215

      Condition Numbers and the Loss of Precision of Linear Equations

    6. No Access

      Chapter

      Pages 217-236

      The Condition Number for Nonlinear Problems

    7. No Access

      Chapter

      Pages 237-259

      The Condition Number in ℙ(H (d))

    8. No Access

      Chapter

      Pages 261-273

      Complexity and the Condition Number

    9. No Access

      Chapter

      Pages 275-296

      Linear Programming

    10. Back Matter

      Pages 297-299

  4. Complexity Classes over the Reals

    1. Front Matter

      Pages 301-301

    2. No Access

      Chapter

      Pages 303-315

      Deterministic Lower Bounds

    3. No Access

      Chapter

      Pages 317-334

      Probabilistic Machines

    4. No Access

      Chapter

      Pages 335-357

      Parallel Computations

    5. No Access

      Chapter

      Pages 359-375

      Some Separations of Complexity Classes

    6. No Access

      Chapter

      Pages 377-384

      Weak Machines

previous Page of 2