Chapter 3

How Far Away Is Infinity?

Jörg Waldvogel

Problem 3

3.1 A First Look · 3.2 Extrapolation · 3.3 The Power Method · 3.4 Second-Order Perturbation Theory · 3.5 Summation Formulas: Real Analysis · 3.6 Summation Formulas: Complex Analysis

Solution is known to 273 digits.

Code

• Maple
   
  • Session: p. 56
     
• Mathematica
   
  • Session: p. 57
  • Examples: pp. 65, 67
  • Figure: 3.1
     
• MATLAB
   
  • Sessions: pp. 50, 51, 64, 71
  • Tables: 3.1, 3.3, 3.4, 3.6
  • Figures: 3.2, 3.3, 3.4
  • Commands: cot (removes a bug in MATLAB 6.5), OperatorNorm, ThirdOrderCorrection, SummationFormula, TrapezoidalSum
     
• PARI/PG (download PARI/GP)
   
  • Session: p. 55
  • Tables: 3.2, 3.5 (row-wise), 3.7 (row-wise)
  • Commands: OperatorNorm, OperatorNormTransformed

Other Material

• John Boersma's proof of the formulas on p. 57

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)