Sparse matrix computations arising in distributed parameter identification

SIAM Journal on Matrix Analysis and Applications

Volumn 20, Issue 4, 1999, Pages 1027-1037

  Vogel, Curtis R ^a  

^a MONTANA STATE UNIVERSITY   (United States)

Author keywords

Conjugate gradient iteration; Distributed parameter identification; Preconditioning; Regularization

Indexed keywords

EID: 0033242223     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897317703     Document Type: Article

References (19)

1. H. T. BANKS AND K. KONISCH, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989.
2. P. BLOMGREN AND T. F. CHAN, Modular Solvers for Constrained Image Restoration Problems, UCLA CAM Report 97-52, Department of Mathematics, Univ. California, Los Angeles, 1997.
3. R. H. CHAN, T. F. CHAN, AND C. K. WONG, Cosine transform based preconditioned for total variation minimization problems in image processing, in Iterative Methods in Linear Algebra II, Proc. 2nd IMACS Internat. Symposium on Iterative Methods in Linear Algebra, Bulgaria, June 1995, IMACS Ser. Comput. Appl. Math. 3, S. Margenov and P. Vassilevski, eds., pp. 311-329.
4. T. F. CHAN, G. H. GOLUB, AND P. MULET, A nonlinear primal-dual method for total variation-based image restoration, in ICAOS '96, 12th Internat. Conf. on Analysis and Optimization of Systems: Images, Wavelets, and PDE's, Paris, June 26-28, 1996, Lecture Notes in Control and Inform. Sci. 219, M. Berger, R. Deriche, I. Herlin, J. Jaffre, and J. Morel, eds., Springer-Verlag, New York, 1996, pp. 241-252.
5. G. CHAVENT AND P. LEMONNIER, Identification de la non-linearité d'une equation parabolique quasilineare, Appl. Math. Optirn., 1 (1974), pp. 121-162.
6. J. W. DANIEL, The conjugate gradient method for linear and nonlinear operator equations, SIAM J. Numer. Anal., 4 (1967), pp. 10-26.
7. J. E. DENNIS, JR. AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
8. D. C. DOBSON AND F. SANTOSA, Recovery of blacky images from noisy and blurred data, SIAM J. Appl. Math., 56 (1996), pp. 1181-1198.
9. C. W. GROETSCH, Inverse Problems in the Mathematical Sciences, Friedr. Vieweg & Sohn, Braunschweig, 1993.
10. M. HANKE, A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems, Inverse Problems, 13 (1997), pp. 79-95.
11. M. HANKE AND P. C. HANSEN, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), pp. 253-315.
12. MATLAB, The Math Works, Inc., Natick, MA, 1997.
13. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS Publishing Co., Boston, MA, 1996.
14. F. SANTOSA AND W. W. SYMES, Computation of the Hessian for least-squares solutions of inverse problems in reflection seismology, Inverse Problems, 4 (1988), pp. 211-233.
15. A. N. TIKHONOV, Regularization of incorrectly posed problems, Soviet Math. Dokl., 4 (1963), pp. 1624-1627.
16. C. R. VOGEL AND M. E. OMAN, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.
17. C. R. VOGEL AND M. E. OMAN, A fast, robust algorithm for total variation based reconstruction of noisy, blurred images, IEEE Trans. Image Process., 7 (1998), pp. 813-824.
18. C. R. VOGEL AND J. G. WADE, Analysis of costate discretizations in parameter estimation for linear evolution equations, SIAM J. Control Optim., 33 (1995), pp. 227-254.
19. A. WEISER AND M. F. WHEELER, On convergence of block-centered finite differences for elliptic problems, SIAM J. Numer. Anal., 25 (1988), pp. 351-375.