January 19, 2019

Numerical and Computational Challenges in Science and Engineering Program

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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