Vol. 05
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
Iterative Methods for Inverse Problems
By
, Vol. 05, 423-454, 1991
Abstract
Citation
A. Roger F. Chapel , "Iterative Methods for Inverse Problems," , Vol. 05, 423-454, 1991.
doi:10.2528/PIER89103102
http://www.jpier.org/PIER/pier.php?paper=8910312
References

1. Moré, J. J., B. S. Gabow, and K. E. Hillstrom, "Testing unconstrained optimization software," ACM Trans. Math. Soft., Vol. 7, 17-41, 1981.

2. Lions, J. L., Controle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Gauthier Villars, Paris, 1968.

3. Roger, A., "Reciprocity theorem applied to the computation of functional derivatives," Electromagnetics, Vol. 2, 69-83, 1982.

4. Levy, A. V. and S. Gomez, "The tunneling algorithm for the global optimization problem of constrained functions,", Technical Report, Universidad National de México, 1980.

5. Rinnooy Kan, A. H. G. and G. T. Tirnmer, "Stochastic Global Optimization methods: Clustering methods," Mathematical Programming, Vol. 39, 27-56, 1987.

6. Kirkpatrick, S., C. D. Crelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, Vol. 220, 671-680, 1983.

7. Fiacco, A. V. and G. P. McCormick, Non Linear Programming: Sequential Unconstrained Minimization Techinques, John Wiley, New York, 1968.

8. Sarkar, T. K., X. Yang, and E. Arvas, "A limited survey of various conjugate gradient methods for solving complex matrix equations arising in Electromagnetic Wave Interaction," Wave Motion, Vol. 10, 527-546, 1988.

9. Tijhuis, A. G., "Born-type reconstruction of material parameters of an inhomogeneous lossy dielectric slab from reflected field data," Wave Motion, Vol. 11, 151-173, 1989.

10. Kennett, B. L. N. and P. R. Williamson, "Subspace methods for large-scale non linear inversion," Mathematical Geophysics, 139-154, Reidel Publishing Co., 1988.

11. D'Aboville, O., "Etude et mise en oeuvre d'un parallelisme multitache en sismique numerique,", Ph.D. dissertation, 1987.

12. Hestesnes, M. and E. Stiefel, "Method of conjugate gradient for solving linear systems," J. Res. Nut. Standards, Vol. 49, 409-436, 1952.

13. Fletcher, R. and C. M. Reeves, "Function minimization by conjugate gradients," Computer Journal, Vol. 7, 149-154, 1964.

14. Polack, E., Computational Methods in Optimization, a Unified Approach, Academic Press, New York, 1971.

15. Van den Berg, "Iterative computational techniques in scattering based on the integrated squared error criterion," IEEE Trans. Antennas Propagat., Vol. 32, 1063-1071, 1984.

16. Roger, A., "Newton Kantorovich algorithm applied to an electromagnetic inverse problem," IEEE Trans. Antennas Propagat., Vol. 29, 232-238, 1981.

17. Powell, M. J. D., "Convergence properties of a class of Minimization Algorithms," Non Linear Programming, Vol. 2, Academic Press, New York, 1975.

18. Broyden, C. G., "A class of methods for solving non linear simultaneous equations," Math Comp., Vol. 19, 577-593, 1965.

19. Buckley, A. and A. Lenir, "QN-like variable storage Conjugate Gradient," Mathematical Programming, 1982.

20. Sorensen, D. C., "Newton's method with a model trust region modification," SIAM J. Numer. Anal., Vol. 19, 409-426, 1982.

21. Moré, J. J., "Recent developments in Algorithms and Software for trust Region methods," Mathematical Programming: the state of the art, 258-287, Springer, 1982.

22. Roger, A., P. Terpolilli, and O. Gosselin, "Trust region methods for seismic inverse problems," World Scientific, 93-103, Singapore, 1989.

23. Shultz, G. A., R. B. Schnabel, and H. R. Byrd, "A family of Trust Region based algorithms for unconstrained minimization with strong global convergence properties," Siam J. Numer. Anal., Vol. 22, 47-67, 1985.

24. Terpolilli, P. and A. Roger, "Trust Region strategies with Quasi-Newton schemes," New Methods in Optimization and their Industrial Uses, ISNM, Vol. 87, Birkhauser, 1989.

25. Levenberg, K., "A method for the solution of certain non linear problems in least squares," Quart. Appl. Math., Vol. 2, 164-168, 1944.

26. Marquardt, D. W., "An algorithm for least squares estimation of non linear parameters," SIAM J. Appl. Math., Vol. 11, 434-441, 1963.

27. Zangwill, W. L., Non Linear Programming: A Unified Approach, Prentice Hall, 1969.

28. Goldstein, A. A., Constructive Real Analysis, Harper, New York, 1967.

29. Wolfe, P., "Convergence conditions for ascent methods," S.I.A.M. Review, Vol. 11, 226-235, 1969.

30. Powell, M. J. D., "Some global convergence properties of a variable metric algorithm for minimization without exact line searches," Non Linear Programming, SIAM-AMS Proceedings 9, Providence, R.I., 1976.

31. Luenberger, D. G., Introduction to Linear and Nonlinear Programming, Addison Wesley, 1973.

32. McCormick, G. P. and K. Ritter, "Alternative proofs of the convergence Properties of the Conjugate Gradient Method," J. Optimization Theory and Appl., Vol. 13, 497-515, 1974.

33. Dennis, J. E. and J. J. Moré, "A characterization of superlinear convergence and its application to Quasi-Newton methods," Mathematics of Computation, Vol. 28, 549-560, 1974.

34. Galan-Malaga, H., D. Lesselier, and W. Tabbara, "Dipole approximations applied to the inverse problem in boreholes: a numerical study," Wave Motion, Vol. 11, 137-150, 1989.

35. Gill, P. E., W. Murray, and M. H. Wright, Practical Optimization, Academic Press, London, 1981.

36. Roger, A. and M. Baribaud, "Optimization and the time-dependent inverse problem," Optique Hertzienne et Diélectriques Meeting, 1989.

37. Roger, A., "Convergence et Stabilité en Sismique inverse," Rapport Elf-Aquitaine, No. 89-445, 1989.

38. Roger, A., D. Maystre, and M. Cadilhac, "On a problem of inverse scattering in Optics: the dielectric inhomogeneous medium," J. Optics, Vol. 9, 83-90, 1978.

39. Tijhuis, A., Electromagnetic Inverse Profiling, VNU Science Press, Utrecht, 1987.

40. Hiebert, K. L., "An Evaluation of Mathematical Software That Solves Nonlinear Least Squares Problems," ACM Trans. Mathematical Software, Vol. 7, No. 1, 1-16, 1981.

41. Gay, D. M., "Subroutines for Unconstrained Minimization using a model/Trust Region Approach," ACM Trans. Mathematical Software, Vol. 9, No. 4, 503-524, 1983.

42. Montarnal, A., "Mise en oeuvre d'une batterie de tests pour algorithmes de minimisation sans contrainte," Elf-Aquitaine Report, No. 87-752, 1987.

43. Hasselot, C. and V. Millet, "Confrontation de divers algorithmes d'optimisation,", D.E.S.S., University of Pau, 1987.

44. Gosselin, O., A. Roger, P. Terpolilli, and J. P. Penot, "Problèmes d'identification: un algorithme robuste et efficace," Congrès National d'Analyse Numérique, 1988.

45. Holberg, O., "Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena," Geophysical Prospecting, Vol. 37, 629-655, 1987.

46. Kolb, P. and G. Canadas, "Least squares inversion of prestack data: simultaneous identification of density and velocity of stratified media," 56th Annual SEG Meeting, Houston, 1986.

47. Jannane, H. N., "The wavelengths of the earth structures that we can resolve from seismic reflection data," ETG Report, Vol. 8, 2.1-2.18, 1987.

48. Richard, V., "High resolution stratigraphic extrapolation: a 1-D inverse problem," 48th E.A.E.G. meeting, Ostend, 1986.

49. Chapel, F., P. Kolb, and G. Canadas, "CMP non linear inversion in (τ, p) domain," 59th Annual SEG Meeting, Houston, 1989.

50. Symes, W. W., "Velocity inversion by coherency optimization," 58th Annual SEG Meeting, Anaheim, 1988.

51. Howard, A. Q. Jr., "Induction logging for vertical structures in the presence of a borehole fluid," Geophys, Vol. 46, No. 1, 68-75, 1981.

52. Roger, A., E. Toro, and D. Maystre, Contract Schlumberger-Aix Marseille III, 1984.

53. Rumsey, V. H., "Reaction concept in Electromagnetic Theory," Phys. Rev., Vol. 94, No. 6, 1483-1491, 1954.

54. Maystre, D., A. Roger, and E. Toro, "Inverse scattering on electromagnetic measurements in a stratified medium," Revue Phys. Appl., Vol. 20, 815-821, 1985.