Accessible Requires Authentication Published by De Gruyter July 2, 2013

A Fast Algorithm for Parameter Identification Problems Based on the Multilevel Augmentation Method

Hui Cao and M. Thamban Nair

Abstract.

A multilevel augmentation method is considered to solve parameter identification problems in elliptic systems. With the help of the natural linearization technique, the identification problems can be transformed into a linear ill-posed operation equation, where noise exists not only in RHS data but also in operators. Based on multiscale decomposition in solution space, the multilevel augmentation method leads to a fast algorithm for solving discretized ill-posed problems. Combining with Tikhonov regularization, in the implementation of the multilevel augmentation method, one only needs to invert the same matrix with a relatively small size and perform a matrix-vector multiplication at the linear computational complexity. As a result, the computation cost is dramatically reduced. The a posteriori regularization parameter choice rule and the convergence rate for the regularized solution are also studied in this work. Numerical tests illustrate the proposed algorithm and the theoretical estimates.

Published Online: 2013-07-02
Published in Print: 2013-07-01

© 2013 by Walter de Gruyter Berlin Boston