Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Prof. Sergei Pereverzyev |
Affiliation | : |
Johann Radon Institute for Computational and
Applied Mathematics, Austria |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
April 8,2008 (Tuesday) |
Title |
: |
The balancing principle for the regularization of elliptic Cauchy problems |
Abstract | : |
EA classical ill-posed
elliptic Cauchy problem is discussed. We consider the reconstruction of the
Dirichlet trace of the solution at the part of a boundary where no data are
available. By natural linearization we transform it into a linear ill-posed
operator equation. Discretization is applied as a regularization method
(also known as a self-regularization) to obtain a stable approximate
solution. Balancing principle as an adaptive strategy is studied to choose
an appropriate discretization level without quantitative knowledge of a
convergent rate or stability. Numerical tests illustrate theoretical
results. |