|Date:||Mon, September 21, 2009|
|Place:||East Hall 2|
Abstract: We will discuss realization and application of a new concept called approximation procedure, called approximate approximations. Most of these procedures, which includes approximate quasi-interpolation, least square approximation, cubature of integral operators, and wavelet approximations, have one common feature. They are accurate without being convergent in a rigorous sense. In numerical mathematics, such a situation is not exceptional. For instance, non-convergent algorithms are natural in solving overdetermined ill-posed problems. However, for the approximation processes mentioned above, convergence is required.
The justification for this new concept is that engineers and researchers who use numerical methods for solving applied problems do not need the convergence of the method. In fact they need result which are exact within a prescribed accuracy determined mainly by the tolerance of measurement and other physical parameters, and always by the precision of the computing system.