### Computational Analysis Seminar

# Zymantas Darbenas

### (Jacobs University)

## "Approximate approximations"

** Date: ** |
Mon, September 21, 2009 |

** Time: ** |
14:00 |

** 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.