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Last Update: 2008-07-01

• "Classical Error Estimation (CEE)" is :
  • a posteriori and empirical error estimation which has been used for long time
  • not regorous but practical one because it does not require to rewrite existed numerical algorithmes
  • to separate round-off error in approximation obtained, so truncation error (theoritical error) in it can be estimated.
  • applicable in IEEE754 double (and fixed) precision) ONLY
  • able to be more accurate if multiple (and mixed) precision arithmetic would be available
  • able to make us calculate the approximation with user-required precision as application of CEE
• How do we apply CEE to arbitrary precision computation ?
• Estimation of Round-off Error
  • IEEE754 double and fixed precision arithmetic ONLY
  • Multiple and mixed precision arithmetic like MPFR/GMP
• Case Study
  • n-th Degree (n = 1, 2, 3, 4) Algebraic Equation
  • Generator of Coefficients of the polynomial which stems from Chebychev integration formula
  1. Source Program in C -> chevcoef.c
  2. Table of coefficients: From 8 to 512th degree, From 20 to 10000 decimal digits (tar.bz2 file)
  3. 1024th degree
  4. 2048th degree
  5. 4096th degree
  6. 8192th degree
  7. 16384th degree -> ex) 1000 correct decimal digits
  8. 32768th degree
  • Linear System
  • Gaussian Quadrature Formulas for Numerical Integration
  • Initial Value Problem for Ordinary Differential Equation

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