Sparse Matrix Computations Arising in Distributed Parameter Identification

A penalized least squares approach known as Tikhonov regularization is commonly used to estimate distributed parameters in partial differential equations. The application of quasi-Newton minimization methods then yields very large linear systems. While these systems are not sparse, sparse matrices play an important role in gradient evaluation and Hessian matrix-vector multiplications. Motivated by the spectral structure of the Hessian matrices, a preconditioned conjugate gradient method is introduced to efficiently solve these linear systems. Numerical results are also presented.