Rick Beatson's publications and downloads

• R. K. Beatson, M. J. D. Powell and A. M. Tan, “Fast evaluation of polyharmonic splines in three dimensions”, IMA Journal of Numerical Analysis 2006; doi: 10.1093/imanum/drl027
  Supplementary results and tables for the above paper.
• R. Vennell and R. K. Beatson, “Moving vessel ADCP measurement of tidal streamfunction using radial basis functions”, Journal of Geophysical Research,, 111, C09002, doi:10.1029/20005JC003321. Preprint (703 kilobyte pdf)
  Note: The above is one way to approximate with divergence free vector fields.
• R. K. Beatson and M. K. Langton, “Integral interpolation”, pp. 199-218 in Algorithms for Approximation V., A. Iske and J. Levesley eds., Springer-Verlag, Heidelberg, 2006. (Typos corrected version 2.48 megabyte pdf)
• R. K. Beatson, H.-Q. Bui and J. Levesley, “Embeddings of Beppo-Levi spaces in Holder-Zygmund spaces and a new method for radial basis function interpolation error estimates”, Journal of Approximation Theory, vol. 137, pp. 166-178, 2005.
• R. K. Beatson, J. B. Cherrie, T. J. McLennan, T. J. Mitchell, J. C. Carr, W. R. Fright and B. C. McCallum, “Surface reconstruction via smoothest restricted range approximation”, pp. 41-52 in Geometric modeling and computing, M. L. Lucian and M. Neamtu eds, Nashboro Press, 2004. (1.2 megabyte pdf)
• R. K. Beatson and H.-Q. Bui, “Mollification formulas and implicit smoothing”, Research report UCDMS 2003/19, December 2003. (2.6 megabyte pdf)
• J. C. Carr, R. K. Beatson, B. C. McCallum, W. R. Fright, T. J. McLennan and T. J. Mitchell, “Smooth surface reconstruction from noisy range data”, in Graphite 2003, ACM Press, New York, 119-126. (1.6 megabyte pdf)
• S. D. Billings, R. K. Beatson and G. N. Newsam, “Interpolation of geophysical data with continuous global surfaces”, in Geophysics, vol 67, pp. 1810-1822, 2002.
• S. D. Billings, G. N. Newsam and R. K. Beatson, “Smooth fitting of geophysical data with continuous global surfaces”, in Geophysics, vol 67, pp. 1823-1834, 2002.
• R. K. Beatson and J. Levesley, “Good point/bad point iterations for solving the thin-plate spline interpolation equations”, in Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 17-25, 2002.
• C. T. Mouat and R. K. Beatson, “On the boundary over distance preconditioner for radial basis function interpolation”, in Algorithms for Approximation IV, University of Huddersfield Press, pp. 252-259, 2002.
• C. T. Mouat and R. K. Beatson, “RBF Collocation” , Research report UCDMS 2002/3, February 2002. (780K pdf)
• J. B. Cherrie, R. K. Beatson, and G. N. Newsam, “Fast evaluation of radial basis functions: Methods for generalized multiquadrics in Rⁿ”, SIAM J. Sci. Comput. , vol. 23, no. 5, pp. 1549-1571, 2002.
• J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans, “Reconstruction and representation of 3D objects with radial basis functions”, in Computer Graphics (SIGGRAPH 2001 proceedings), pp. 67-76, August 2001. (1.3 megabyte pdf)
• C. T. Mouat and R. K. Beatson, “Some properties of the boundary over distance preconditioner for radial basis function interpolation”, Research report UCDMS 2001/6, July 2001. (1.1 megabyte pdf)
• R. K. Beatson, J. B. Cherrie, and D. L. Ragozin, “Fast evaluation of radial basis functions: Methods for four-dimensional polyharmonic splines”, SIAM J. Math. Anal., vol. 32, no. 6, pp. 1272-1310, 2001.
• R. K. Beatson, W. A. Light, and S. Billings, “Fast solution of the radial basis function interpolation equations: Domain decomposition methods”, SIAM J. Sci. Comput., vol. 22, no. 5, pp. 1717-1740, 2000.
• R. K. Beatson, J. B. Cherrie, and D. L. Ragozin, “Polyharmonic splines in R^d : Tools for fast evaluation”, in Curve and Surface Fitting: Saint Malo 1999 (A. Cohen, C. Rabut, and L. L. Schumaker, eds.), pp. 47-56, Vanderbilt University Press, Nashville, 2000.
• R. K. Beatson and E. Chacko, “Fast evaluation of radial basis functions: A multivariate momentary evaluation scheme”, in Curve and Surface Fitting: Saint Malo 1999 (A. Cohen, C. Rabut, and L. L. Schumaker, eds.), pp. 37-46, Vanderbilt University Press, Nashville, 2000.
• R. K. Beatson, J. B. Cherrie, and C. T. Mouat, “Fast fitting of radial basis functions: Methods based on preconditioned GMRES iteration”, Advances in Computational Mathematics, vol. 11, pp. 253-270, 1999. (4 megabyte pdf from scan)
• R. K. Beatson and G. N. Newsam, “Fast evaluation of radial basis functions: Moment based methods”, SIAM J. Sci. Comput., vol. 19, pp. 1428-1449, 1998.
• R. K. Beatson and L. Greengard, “A short course on fast multipole methods”, in Wavelets, Multilevel Methods and Elliptic PDEs (M. Ainsworth, J. Levesley, W. Light, and M. Marletta, eds.), pp. 1-37, Oxford University Press, 1997.
• J. C. Carr, W. R. Fright, and R. K. Beatson, “Surface interpolation with radial basis functions for medical imaging”, IEEE Trans. Medical Imaging, vol. 16, pp. 96-107, February 1997. (1.2 megabyte .ps.gz)
• R. K. Beatson and W. A. Light, “Fast evaluation of radial basis functions: Methods for two-dimensional polyharmonic splines”, IMA Journal of Numerical Analysis, vol. 17, pp. 343-372, 1997.
• R. K. Beatson, G. Goodsell, and M. J. D. Powell, “On multigrid techniques for thin-plate spline interpolation in two dimensions”, Lectures in Applied Mathematics, vol. 32, pp. 77-97, 1996.
• R. K. Beatson and N. Dyn, “Multiquadric B-splines”, J. Approximation Theory, vol. 87, pp. 1-24, 1996.
• R. K. Beatson and M. J. D. Powell, “An iterative method for thin-plate spline interpolation that employs approximations to the Lagrange functions”, in Numerical Analysis 1993 (D. F. Griffiths and G. A. Watson, eds.), pp. 17-39, Longmans, Harlow, 1994.
• R. K. Beatson and W. A. Light, “Quasi-interpolation by thin-plate splines on the square”, Constr. Approx., vol. 9, pp. 343-372, 1993.
• R. K. Beatson and G. N. Newsam, “Fast evaluation of radial basis functions: I”, Computers Math. Applic., vol. 24, no. 12, pp. 7-19, 1992. (3 megabyte pdf from scan)
• R. K. Beatson and W. A. Light, “Quasi-interpolation in the absence of polynomial reproduction”, in Numerical Methods of Approximation Theory (D. Braess and L. L. Schumaker, eds.), vol. 105 of ISNM, pp. 21-39, Birkhauser Verlag, 1992.
• R. K. Beatson and E. Chacko, “Which cubic spline should one use”, SIAM J. on Scientific and Statistical Computation, vol. 13, pp. 1009-1024, 1992.
• R. K. Beatson and M. J. D. Powell, “Univariate multiquadric approximation: quasi interpolation to scattered data”, Constr. Approx., vol. 8, pp. 275-288, 1992.
• R. K. Beatson and M. J. D. Powell, “Univariate interpolation on a regular grid by a multiquadric plus a linear polynomial”, IMA J. of Numerical Anal., vol. 12, pp. 107-133, 1992.
• R. K. Beatson and H. Wolkowicz, “Post-processing piecewise cubics for monotonicity”, SIAM J. Numer. Anal, vol. 26, pp. 480-502, 1989.
• R. K. Beatson and E. Chacko, “A quantitative comparison of end conditions for cubic spline interpolation”, in Approximation Theory IV (C. K. Chui, ed.), pp. 77-79, Academic Press, 1989.
• R. K. Beatson, “On the convergence of some cubic spline interpolation schemes”, SIAM J. Numer. Anal., vol. 23, pp. 903-912, 1986.
• R. K. Beatson and Z. Ziegler, “Monotonicity preserving surface interpolation”, SIAM J. Numer. Anal., vol. 22, pp. 401-411, 1985.
• R. K. Beatson and D. Leviatan, “On comonotone approximation”, Canad. Math. Bull., vol. 26, pp. 220-224, 1983.
• R. K. Beatson, “Monotone and convex approximation by splines: Error estimates and a curve fitting algorithm,” SIAM J. Numer. Anal., vol. 19, pp. 1278-1285, 1982.
• R. K. Beatson, “Best monotone approximation by reciprocals of polynomials”, J. Approx. Theory, vol. 36, pp. 99-103, 1982.
• R. K. Beatson, “Restricted range approximation by splines and variational inequalities”, SIAM J. Numer. Anal., vol. 19, pp. 372-380, 1982.
• R. K. Beatson, C. K. Chui, and M. Hasson, “Degree of best inverse approximation by polynomials”, Illinois J. Math., vol. 27, pp. 173-180, 1982.
• R. K. Beatson, “Convex approximation by splines”, SIAM J. Math. Anal., vol. 12, pp. 549-559, 1981.
• R. K. Beatson and C. K. Chui, “Best multipoint local approximation”, in Functional Analysis and Approximation (P. L. Butzer, B. Sz.-Nagy, and E. Gorlich, eds.), vol. 60 of ISNM, pp. 283-296, Birkhauser Verlag, 1981.
• R. K. Beatson, “On the degree of approximation with Hermite interpolatory side conditions”, J. Approx. Theory, vol. 28, pp. 197-206, 1980.
• R. K. Beatson, “Joint approximation of a function and its derivatives”, in Approximation Theory III (E. W. Cheney, ed.), pp. 199-206, Academic Press, 1980.
• R. K. Beatson, “The degree of approximation by polynomials increasing to the right of the interval”, J. Approx. Theory, vol. 26, pp. 151-158, 1979.
• R. K. Beatson, “Degree of approximation of differentiable functions by reciprocals of polynomials on [0,∞)”, J. Approx. Theory, vol. 27, pp. 33-44, 1979.
• R. K. Beatson, “Jackson type theorems for approximation with Hermite-Birkhoff interpolatory side conditions”, J.Approx. Theory, vol. 22, pp. 95-104, 1978.
• R. K. Beatson, “The degree of monotone approximation”, Pacific J. Math., vol. 74, pp. 5-14, 1978.
• R. K. Beatson, “The asymptotic cost of Lagrange interpolatory side conditions”, J. Approx. Theory, vol. 20, pp. 228-295, 1977. Addendum loc. cit. vol. 29, 1980, pp. 336-338.