Title: A parallel method for backward parabolic problems based on the Laplace 
transformation.

Abstract: A parallel method for time-discretization of backward
parabolic problems is proposed. The problem is reformulated to a set
of Helmholtz type problems with a parameter on a suitably chosen
contour in the complex plane. After solving the resulting elliptic
equations, which can be solved in parallel, we obtain a regularized
solution with high frequency terms cut off by the inverse Laplace
transforms without requiring the knowledge of the eigenfunctions of
the differential operator.  Since the regularized solution is obtained
without artificial perturbation and high frequency components of the
noise are suppressed, the quality of the solution is improved
significantly compared to those obtained by the other methods.  Two
different numerical inversions of Laplace transforms, with arbitrary
high order of accuracy, and the spectral accuracy, respectively, are
used.  Error estimates and numerical examples are presented.

This talk will be based on the paper jointly written by Jinwoo Lee (KIAS,
Seoul, Korea) that will appear in SIAM J. Numer. Anal.