RANDOM  INTERPOLATION

References & Web Links

  1. F. Acton, Numerical Methods That Work, American Mathematical association, 1990.
  2. T.M. Apostol, Calculus, Vol. II, Academic Press, 1962.
  3. S.J. Yakowitz, Computational Probability and Simulation, Addison- Wesley, 1977.
  4. A. Ralston and H, Wilf, Mathematical Methods for Digital Computers, Wiley, 1960.
  5. D. Gillespie, The Monte Carlo Method of Evaluating Integrals, ADA-005891, DTIC, 1975.
  6. P. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1930.
  7. J.D. Jackson, Classical Electrodynamics, John-Wiley, 1962.
  8. B. van der Pol and H. Bremmer, Operational Calculus, Cambridge University Press, 1955.
  9. A. Zemanian, Distribution Theory and Transform Analysis, McGraw-Hill, 1965.
  10. G. Arfken, Mathematical Methods for Physicists, Academic Press, 1970.
  11. M. Lighthill, Fourier Analysis and Generalized Functions, Cambridge University Press, 1958.
  12. Donald Shepard, A two-dimensional interpolation function for irregularly-spaced data, Proceedings of the 23rd ACM national conference, p.517-524, January 1968
  13. R. Franke, A critical comparison of some methods for interpolation of scattered data. Tech. Rep. NPS-53-79-003, Dept. of Mathematics, Naval Postgraduate School, Monterey, Calif., 1979.
  14. R. Franke, Scattered data interpolation: tests of some methods, Math. Comp., Vol.48 (1982), pp.181--200.
  15. R.J. Renka, Multivariate interpolation of large sets of scattered data, ACM Trans. on Math. Software 14:2, June 1988, pp. 139-148
  16. Michael W. Berry , Karen S. Minser, Algorithm 798: high-dimensional interpolation using the modified Shepard method, ACM Transactions on Mathematical Software (TOMS), v.25 n.3, p.353-366, Sept. 1999
  17. Dirac Delta Function, 2003, http://www.chm.uri.edu/urichm/chm532/delta/node4.html
  18. Dirac Delta Function, 2003, http://www.phy.auckland.ac.nz/Staff/smt/453701/chap1_00.pdf
  19. Monte-Carlo Method, 2002, http://unicast.org/enclosure/text.pdf
  20. Reproducing Kernel Hilbert Space (RKHS) method and references, 1998, http://www.dur.ac.uk/j.m.hutson/ccp6-98/node30.html#w46, and http://www.dur.ac.uk/j.m.hutson/ccp6-98/node28.html
  21. W.H. Prest et al., Numerical Recipes in C (The art of scientific computing), 1988-1992, Cambridge University Press, http://www.ulib.org/WebRoot/Books/Numerical+recipes/bookcpdf/c7-6.pdf
  22. Markus Hegland, Computational challenges in data mining, ANZIAM J. 42 (E) ppC1-C43, 2000
  23. S. Mckinley and M. Levine, Cubic Spline Interpolation,1998, http://online.redwoods.cc.ca.us/instruct/darnold/laproj/Fall98/SkyMeg/splinepres/sld037.htm
  24. Rational Function Model, http://www.itl.nist.gov/div898/handbook/pmd/section6/pmd642.htm
  25. David Flanagan, Paula Ferguson (Editor), JavaScript: The Definitive Guide, 2001, O'Reilly & Associates, Incorporated
  26. Elizabeth Castro, HTML 4 for the World Wide Web: Visual QuickStart Guide, 1999, Peachpit Press
  27. J. Hertz, A. Krogh, and R. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, 1991
  28. Benjamin K.K. Fang, Dirac Delta Function and Interpolation, Physics Computing 1991 conference, San Jose, June 1991. Sponsored by American Physical Society.
  29. P. Alfeld, "Scattered Data Interpolation in Three or More Variables", Mathematical Methods in Computer Aided Geometric Design, T. Lyche, L. Schumacher, eds., Academic Press, 1989, p.1-34.
  30. T. Poggio and F. Girosi, "A Theory of Networks for Approximation and Learning", A.I. Memo NO. 1140, Artificial intelligence Lab, M.I.T. July 1989.
  31. Mira Bozzini and Milvia Rossini, "Testing Methods for 3 D Scattered Data Interpolation", Monografias de la Academia de Ciencias de Zaragoza.20:111 –135,(2002).
  32. R. Franke, "Scattered data interpolation.Test of some methods". Mathematics of Computation ,48:181 –199,1982.
  33. T.A.Foley, "Interpolation and approximation of 3-d and 4-d scattered data". Comput. Math.Appl.,13:711 –740,1987.
  34. Damiana Lazzaro and Laura B.Montefusco, "Radial Basis Functions for the Multivariate Interpolation of Large Scattered Data Sets", Journal of Computational and Applied Mathematics, 2002, pp. 521--536. [3D, 30,000 points]
  35. Lall, U., Y. Moon, and K. Bosworth, "Kernel Flood Frequency Estimators: Bandwidth Selection and Kernel Choice." Water Resources Research , April 1993.
  36. Nadaraya, E. A. On estimating regression. Theory of Probability and Its Applications, Vol. 9, 1964, pp. 141-142.
  37. Watson, G. S. Smooth regression analysis. Sankhya Series A, Vol. 26, 1964, pp. 359-372.
  38. Hardle, W. Applied nonparametric regression. Cambridge University Press, New York, 1990
  39. http://www.statoek.wiso.uni-goettingen.de/veranstaltungen/ast/assign/ast_part2.pdf
  40. Silverman, B. (1986): Density Estimation for Statistics and Data Analysis. New-York, Chapman and Hall.
  41. Ruppert, D. & Wand, M. P. (1994). Multivariate locally weighted least squares regression, Annals of Statistics 22(3): 1346-1370.
  42. Halton, J.H., On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960), 84-90.
  43. Niederreiter, H. & P. Hellekalek & G. Larcher & P. Zinterhof, Eds. (1998): "Monte Carlo and Quasi-Monte Carlo Methods 1996", Springer-Verlag New York, Lectures Notes in Statistics, 1998, 448 pp.
  44. David L. Donoho, High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality, (2000), http://www-stat.stanford.edu/~donoho/Lectures/AMS2000/Curses.pdf
  45. Wand, M. P. & Jones, M. C. (1995). Kernel Smoothing, Vol. 60 of Monographs on Statistics and Applied Probability, Chapman and Hall, London
  46. Mira Bozzini and Milvia Rossini, Testing Methods for 3 D Scattered Data Interpolation, Monografias de la Academia de Ciencias de Zaragoza. 20:111 –135, (2002). [3375 points 3D]
  47. R.L.Hardy, Multiquadric equations of topography and other irregular surfaces. J. Geophys.Res.,76:1905 –1915,1971.
  48. Shepard, D., 1968, A Two-Dimensional Interpolation Functions for Irregularly Spaced Data, Proc. 23 Nat. Conf. ACM, 517-524.
  49. The central information server for GIS and Spatial Statistics, AI-GEOSTATS
  50. Alfeld, P., Scattered Data Interpolation in Three or More Variables, in Tom Lyche and Larry L. Schumaker (eds), ``Mathematical Methods in Computer Aided Geometric Design'', Academic Press, 1989, 1-34.
  51. Robert J. Luxmoore et al., Signal-transfer modeling for regional assessment of forest responses to environmental changes in the southeastern United States, Environmental Modeling and Assessment 5 (2000) 125-137.
  52. 59th ARFTG Conference Digest, pp. 31-36, June 7, 2002, Seattle, WA Artificial Neural Network Model for HEMTs Constructed from Large-Signal Time-Domain Measurements * Dominique M. M.-P. Schreurs et al.,
  53. George ElKoura and Karan Singh, Handrix: Animating the Human Hand, Eurographics/SIGGRAPH Symposium on Computer Animation (2003), D. Breen, M. Lin (Editors).
  54. Steve Lawrence et al., Function Approximation with Neural Networks and Local Methods: Bias, Variance and Smoothness, Australian Conference on Neural Networks, ACNN 96, Edited by Peter Bartlett, Anthony Burkitt, and Robert Williamson, Australian National University, pp. 16–21, 1996.
  55. Scientific Computing World, Issue 73, 2003.[CERN high energy physics lab in Europe will generate about 12 petabytes, 1015 bytes, (more than 20 million CDs) of data each year.]
  56. I.F.Akyildiz, W.Su,Y.Sankarasubramaniam, E.Cayirci, Wireless sensor networks: a survey, Computer Networks 38 (2002)393 –422
  57. W. Härdle, M. Müller, S. Sperlich, A. Werwatz, Nonparametric and Semiparametric Models, http://www.xplore-stat.de/ebooks/ebooks.html, 2004
  58. I. Ibragimov, and R.Z. Khasminskii (1981) Statistical estimation: asymptotic theory. New York, Springer
  59. Steve Lawrence, et al., Function Approximation with Neural Networks and Local Methods: Bias, Variance and Smoothness, Australian Conference on Neural Networks, ACNN 96, Edited by Peter Bartlett, Anthony Burkitt, and Robert Williamson, Australian National University, pp. 16–21, 1996.
  60. K. Hornik, M. Stinchcombe, and H. White, Multilayer feedforward networks are universal approximators, Neural Networks, 1:75–89, 1988.
  61. R.J. Renka, Multivariate interpolation of large sets of scattered data, ACM Trans. Math. Software 14 (1988) 139-148. (5-D)
  62. Krishnamurti, T.N. and Bounoua, L., 1996. Numerical weather prediction techniques. CRC press.
  63. Barnes, S.L., 1964: A technique for maximizing details in numerical weather map analysis. J. Appl. Meteorol., 3, 396-409.
  64. Quantitative Precipitation Estimation and Segregation Using Multiple Sensors, http://www.norman.noaa.gov/publicaffairs/backgrounders/backgrounder_qpe.html
  65. CPU-instruction, http://csep1.phy.ornl.gov/ca/node3.html
  66. Bob Stine and Dean Foster.(1999), Variable Selection in Credit Modelling, http://www-stat.wharton.upenn.edu/~bob/research/baltimore.pdf
  67. Peter C. Chu, Michael D. Perry, Satellite Data Assimilation for Improvement of Naval Undersea Capability, Naval Ocean Analysis and Prediction Laboratory, Department of Oceanography Naval Postgraduate School, Monterey, CA 93943, http://www.oc.nps.navy.mil/~chu/web_paper/mtsj/undersea.pdf., (GDEM was generated using over seven million temperature and salinity observations)
  68. W S C Williams, Nuclear and Particle Physics, Oxford University Press, 1991
  69. George ElKoura, and Karan Singh, Handrix: Animating the Human Hand, Eurographics/SIGGRAPH Symposium on Computer Animation (2003), D. Breen, M. Lin (Editors)
  70. Damiana Lazzaro and Laura B.Montefusco, Radial Basis Functions for the Multivariate Interpolation of Large Scattered Data Sets, Department of Mathematics,University of Bologna, P.za di Porta S.Donato,5 40127 Bologna -Italy (2002)
  71. http://www.physics.orst.edu/~tate/COURSES/ph320/worksheets/delta.pdf, Dirac delta function.
  72. Mario Koeppen, The curse of dimensionality, http://www.npt.nuwc.navy.mil/Csf/publ.html#koeppen2000
  73. FANG, INC., Supplementary Material for Random Data Interpolation, http://www.fanginc.com/rdic/texas2.doc, 2005
  74. FANG, INC., 2003 NSF Proposal,
  75. FANG, INC., 2004 NSF Proposal,
  76. FANG, INC., SIC Exercise 2004 Manuscript

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