Numerical and Computational Challenges
in Science and Engineering Program
Lecture
June 17, 10:00 am
Gregory Litvinov, International Sophus Lie Centre
Interval Computations and the Effects of Error Autocorrection
The most actual problem in interval analysis is to get realistic interval
estimates for calculating errors, i.e. to get efficient estimates close
to the virtual calculation errors. Difficulties arise if intermediate
errors compensate each other. This is the case of the error autocorrection
effect. In the talk this effect is discussed in details for calculation
of values of real smooth functions by means of rational approximations.
The effect occurs in efficient methods of rational approximation (e.g.,
best appriximations, Pade approximations, linear and nonlinear Pade-Chebyshev
approximations). In this case very significant errors in coefficions
do not affect the accuracy of the approximation. The thing is that the
errors in the coefficients of the corresponding rational approximant
are not distributed in an arbitrary way but form all the coefficients
of a new approximant to the approximated function. The effect of error
autocorrection occurs in the method of least squares and some other
popular methods. This effect is typical for ill-posed problems.
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