Chapter 6

Biasing for a Fair Return

Folkmar Bornemann

Problem 6

6.1 A First Look · 6.2 Using Numerical Linear Algebra · 6.3 Expectations · 6.4 Reducing the Complexity · 6.5 The Joy of Special Functions · 6.6 Using Fourier Analysis · 6.7 Harder Problems

Solution is known to more than 10,002 digits.

Code

• Maple
   
  • Sessions: pp. 132, 134
     
• Mathematica (supporting code is included as initialization cells)
   
  • Sessions: pp. 124 (as alternative to MATLAB), 131, 133, 136, 137, 139, 145, 146
  • Table: 6.1
  • Function: BesselITilde
     
• MATLAB
   
  • Sessions: pp. 124/125, 128, 129, 141
  • Figures: 6.1 (left), 6.1 (right), 6.2
  • Commands: AGM, ReturnProbability, OccupationProbability, ExpectedVisitsExtrapolated, WynnEpsilon
     
• MATLAB/INTLAB (download INTLAB)
   
  • Session: p. 138
  • Commands: AGM, IntervalBisection, subdivide1D

Movie

A sample walk

Links

• Complete Elliptic Integral of the First Kind · Arithmetic-Geometric Mean · Modified Bessel Function of the First Kind. From functions.wolfram.com―A Wolfram Web Resource.
   
• Eric W. Weisstein. Complete Elliptic Integral of the First Kind · Arithmetic-Geometric Mean · Modified Bessel Function of the First Kind. From MathWorld―A Wolfram Web Resource.

Supplements

• Folkmar Bornemann. Formula (6.16) Revisited: Obtaining the Generating Function by a Holonomic Differential Equation. Note of Mar 9, 2007. (accompanying: Maple worksheet, Matlab code)

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: 03/09/07 13:24 +0100 (FB)