Maximum entropy approximation

AIP Conference Proceedings

Volumn 803, Issue , 2005, Pages 337-344

  Sukumar, N ^a  

^a University of California   (United States)

Author keywords

Convex approximation; Information theory; Meshfree methods; Relative entropy

Indexed keywords

EID: 33751231717     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.2149812     Document Type: Conference Paper

References (34)

1. M. Meyer, H. Lee, A. Barr, and M. Desbrun, Journal of Graphics Tools, 7, 13-22 (2002).
2. M.S. Floater, Computer Aided Geometric Design, 20, 19-27 (2003).
3. M. S. Floater, and K. Hermann, "Surface Parameterization: a Tutorial and Survey," in Advances in Multiresolution for Geometric Modelling, edited by N. A. Dodgson, M. S. Floater, and M. A. Sabin, Mathematics and Visualization, Springer, Berlin, Heidelberg, 2005, pp. 157- 186.
4. N. Sukumar, and A. Tabarraei, Int. J. Num. Meth. Engg., 61, 2045-2066 (2004).
5. P. Lancaster, and K. Salkauskas, Mathematics of Computation, 37, 141- 158 (1981).
6. R. Sibson, Mathematical Proceedings of the Cambridge Philosophical Society, 87, 151-155 (1980).
7. N. H. Christ, R. Friedberg, and T. D. Lee, Nuclear Physics B, 210, 337-346 (1982).
8. M. D. Buhmann, Acta Numerica, 9, 1-38 (2000).
9. C. E. Shannon, The Bell Systems Technical Journal, 27, 379-423 (1948).
10. E. T. Jaynes, Physical Review, 106, 620-630 (1957).
11. N. Sukumar, Int. J. Num. Meth. Engg., 61, 2159-2181 (2004).
12. N. Sukumar, and E. A. Maisch, Archives of Computational Methods in Engineering (2005), in press.
13. M. R. Gupta, An Information Theory Approach to Supervised Learning, Ph.D. thesis, Department of Electrical Engineering, Stanford University, Palo Alto, CA, U.S.A. (2003).
14. M. Arroyo, and M. Ortiz, Int. J. Num. Meth. Engg. (2005), in press.
15. R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
16. G. Strang, and G. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973.
17. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, Computer Methods in Applied Mechanics and Engineering, 139, 3-47 (1996).
18. S. Li, and W. K. Liu, Applied Mechanics Review, 55, 1-34 (2002).
19. S. N. Atluri, and S. Shen, The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press, Encino, CA, 2002.
20. G. R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, Boca Raton, FL, 2003.
21. S. Li, and W. K. Liu, Meshfree Particle Methods, Springer-Verlag, New York, NY, 2004.
22. E. Cueto, N. Sukumar, B. Calvo, M. A. Martínez, J. Cegon̈ino, and M. Doblaré, Archives of Computational Methods in Engineering, 10, 307-384 (2003).
23. A. Khinchin, Mathematical Foundations of Information Theory, Dover, New York, NY, 1957.
24. E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge, UK, 2003.
25. N. Agmon, Y. Alhassid, and R. D. Levine, Journal of Computational Physics, 30, 250-258 (1979).
26. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran: The Art of Scientic Computing, Cambridge University Press, New York, NY, 1992, second edn.
27. V. T. Rajan, Discrete and Computational Geometry, 12, 189-202 (1994).
28. S. Kullback, Information Theory and Statistics, Wiley, New York, NY, 1959.
29. J. E. Shore, and R. W. Johnson, IEEE Transactions on Information Theory, 26, 26-36 (1980).
30. S. Kullback, and R. A. Leibler, Annals of Mathematical Statistics, 22, 79-86 (1951).
31. D. Shepard, "A Two-Dimensional Interpolation Function for Irregularly Spaced Points," in ACM National Conference, 1968, pp. 517-524.
32. J. Bakerjarvis, Journal of Mathematical Physics, 30, 302-306 (1989).
33. J. Bakerjarvis, M. Racine, and J. Alameddine, Journal of Mathematical Physics, 30, 1459-1463 (1989).
34. E. D. Malaza, H. G. Miller, and A. R. Plastino, Physica A, 265, 224-234 (1999).