Sparse Matrix Computations Arising in Distributedparameter Identificationcurtis

A penalized least squares approach known as Tikhonov regularization is commonly used to estimate distributed parameters in partial diierential 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 eeciently solve these linear systems. Numerical results are presented.