MULTISCALE PARAMETRIZATION FOR THE ESTIMATION OF A DIFFUSION COEFFICIENT IN ELLIPTIC AND PARABOLIC PROBLEMS

Abstract

The estimation a the diffusion coefficient in elliptic and parabolic equation is known to be an illposed problem. We investigate the effect of a simple change of basis in the parameter space on the behaviour of a Quasi-Newton optimization algorithm used to solve a discretized version of this problem by minimum least squares. We compare the usual local basis used for the representation of fuctions to the multiscale Haar basis. Numerical results show surprisingly better results when the multiscale basis is used. We try to analyse this by looking at the Hessian of the error function in the two basis.