Chapter 4

Think Globally, Act Locally

Stan Wagon

Problem 4

4.1 A First Look · 4.2 Speedy Evolution · 4.3 Interval Arithmetic · 4.4 Calculus · 4.5 Newton's Method for Intervals · 4.6 A Validation Method for Roots · 4.7 Harder Problems · 4.8 Summary

Solution is known to more than 10,002 digits.

Code

• Mathematica
   
  • Sessions: pp. 78, 80, 82, 84, 85, 91, 94, 99
  • Table: 4.1
  • Figures: 4.1–4.8
  • Package with implementation of all the algorithms with bells and whistles
     
• MATLAB/INTLAB (download INTLAB)
   
  • Session: p. 85 (as alternative to Mathematica, see also p. 274)
  • Commands: LowestCriticalPoint, subdivide2D, fun

Packages for Interval Arithmetic

• INTLAB (a MATLAB package)
   
• INTPAKX (a Maple package)
   
• SMATH (written in C)

Packages for Global Optimization

• MathOptimizer (a Mathematica package using random search algorithms)
   
• COCONUT (using interval methods)
   
• GlobSol (using interval methods)

This is a web page for the book:

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing. Society of Industrial and Applied Mathematics (SIAM), Philadelphia, 2004.

last modified: 05/25/04 17:02 +0200 (FB)