Applied Interval Analysis

1. Front Matter

   Pages i-xvi

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 3-7

3. Tools

   1. Front Matter

      Pages 9-9

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   2. Interval Analysis

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 11-43

   3. Subpavings

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 45-63

   4. Contractors

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 65-101

   5. Solvers

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 103-137

4. Applications

   1. Front Matter

      Pages 139-139

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   2. Estimation

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 141-185

   3. Robust Control

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 187-223

   4. Robotics

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 225-268

5. Implementation

   1. Front Matter

      Pages 269-269

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   2. Automatic Differentiation

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 271-286

   3. Guaranteed Computation with Floating-point Numbers

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 287-299

   4. Do It Yourself

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

      Pages 301-351

6. Back Matter

   Pages 353-379

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At the core of many engineering problems is the solution of sets of equa­ tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un­ knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed. This means, for example, that the actual global minimum of a cost function may not be reached, or that some global minimizers of this cost function may escape detection. By contrast, interval analysis makes it possible to obtain guaranteed approximations of the set of all the actual solutions of the problem being considered. This, together with the lack of books presenting interval techniques in such a way that they could become part of any engineering numerical tool kit, motivated the writing of this book. The adventure started in 1991 with the preparation by Luc Jaulin of his PhD thesis, under Eric Walter's supervision. It continued with their joint supervision of Olivier Didrit's and Michel Kieffer's PhD theses. More than two years ago, when we presented our book project to Springer, we naively thought that redaction would be a simple matter, given what had already been achieved . . .

• Interval analysis
• calculus
• control engineering
• estimation
• non-linear equation
• numerical methods
• robot
• robotics
• robustness
• sets

From the reviews:
"Applied Interval Analysis is the right book at the right time to move computing with intervals into the mainstream of engineering, financial, and scientific computing."
G. William Walster, Interval Technology Engineering Manager, Sun Microsystems and Member of the Editorial Board of Reliable Computing

• Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

  Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

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