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
- Source Program in C -> chevcoef.c
- Table of coefficients: From 8 to 512th degree, From 20 to 10000 decimal digits (tar.bz2 file)
- 1024th degree
- 2048th degree
- 4096th degree
- 8192th degree
- 16384th degree -> ex) 1000 correct decimal digits
- 32768th degree
- Linear System
- Gaussian Quadrature Formulas for Numerical Integration
- Initial Value Problem for Ordinary Differential Equation