A preconditioning technique for a class of PDE-constrained optimization problems
Advances in Computational Mathematics
Optimization methods for calibration of heat conduction models
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
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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.