Larry L. Schumaker

Stevenson Professor of Mathematics
Office: Stevenson Center 1532
Phone: (615) 322-6652
Email:mailto:s@mars.cas.vanderbilt.edu

Genealogy

• Advisor Tree

Course Pages

• Honors 182

Conference Organization

• Tenth International Conference on Approximation Theory, St. Louis, March 26--29, 2001
• IMA Workshop on CAGD, Minneapolis, April 23--27, 2001
• Special Session on Sphere Approximation Chatanooga, Oct. 5-6, 2001
• Curve and Surfaces Saint Malo, June 27 - July 3, 2002
• Foundations of Computational Math Minneapolis, August 5--14, 2002.

Other Conferences

• Trends in Approximation Theory, Nashville, May 17--20 , 2000
• Mathematical Methods for Curves and Surfaces, Oslo, June 29 - July 4, 2000
• Algorithms for Approximation IV, Huddersfield, July 16--20, 2001
• Multivariate Approximation Almunecar, Sept. 10--14, 2001
• New Zealand Approximation Conference, Feb. 19 -- 22, 2002, Westport, NZ
• Constructive Function Theory, Varna, June 19--23, 2002
• SIAM 50th Anniversary Conference Philadelphia, July 8--12, 2002.
• PDE on Sphere Toronto, Aug. 12--15, 2002.
• Geodesy OSU, Oct. 1--5, 2002.
• Army Conference Orlando, December 2 - 5, 2002.

Short Vita

Research Interests

• Approximation Theory (Splines)
• CAGD
• Numerical Analysis

Publications

• Complete List of Papers
• Complete List of Books

Recent Papers

1995:

• Circular Bernstein-Bezier Polynomials, (with Peter Alfeld and Mike Neamtu), in Mathematical Methods in CAGD, M. Daehlen, T. Lyche, and L. L. Schumaker (eds), Vanderbilt University Press, 1995, 1--10. (Click for ps)
• Control Curves and Knot Insertion for Trigonometric Splines, with P.E. Koch, M. Neamtu, and Tom Lyche, Adv. Comp. Math. {\bf 3} (1995), 405--424. (Click for ps)

  1996:

• Multi--patch parametric surfaces with minimal energy, with Greg Fasshauer, Comp. Aided. Geom. Design {\bf 13} (1996), 45--79.
• Bernstein-Bezier Polynomials on Spheres and Sphere-Like Surfaces (with Peter Alfeld and Mike Neamtu), CAGD 13 (1996), 333--349. (Click for ps)
• Dimension and Local Bases of Homogeneous Spline Spaces (with Peter Alfeld and Mike Neamtu), SIAM J. Math. Anal. 27 (1996), 1482--1501. (Click for ps)
• Fitting scattered data on sphere-like surfaces using spherical splines (with P. Alfeld and M. Neamtu), J. Comp. Appl. Math. 73 (1996), 5--43. (Click for ps)
• Hybrid Bezier Patches on Sphere-Like Surfaces (with Xiaoyu Liu), J. Comp. Appl. Math. 73 (1996), 157--172. (Click for ps)
• Shape-preserving Knot Removal (with S. Stanley), Comp. Aided Geom. Design {\bf 13} (1996), 851--872. (Click for ps)
• Total positivity properties of LB-splines, with Tom Lyche, in Total Positivity and Its Applications, M. Gasca and C. Micchelli (eds.), Kluwer, Dordrecht, 1996, 35--46.

  1997

• Scattered Data Interpolation Using C^2 Supersplines of Degree Six (with M.-J. Lai) SIAM J. Numer. Anal. 34 (1997), 905--921. (Click for ps)
• Fitting monotone surfaces to scattered data using $C^1$ piecewise cubics, with Lu Han, SIAM J. Numer. Anal. {\bf 34} (1997), 569--585.

  1998

• Scattered Data Fitting on the Sphere (with Greg Fasshauer) Mathematical Methods for Curves and Surfaces II, M. Daehlen, T. Lyche, and L. L. Schumaker (eds.), Vanderbilt Univ. Press, 1998, 117--166. (Click for ps)
• Designing NURBS Cam Profiles using Trigonometric Splines (with M. Neamtu and H. Pottmann), ASME J. Mech. Design. {\bf 120} (1998), 175--180. (Click for ps)
• Quasi-interpolants Based on Trigonometric Splines (with S. Stanley and T. Lyche), J. Approx. Th. 95 (1998), 280--309. (Click for ps)
• On the Approximation Power of Bivariate Splines (with M.-J. Lai), Adv. in Comp. Math. 9 (1998), 251--279. (Click for ps)

  1999

• Dual Focal Splines and Rational Curves with Rational Offsets (with M. Neamtu and H. Pottmann), Mathematical Engineering in Industry 7 (1999), 139--154. (Click for ps)
• On the Approximation Power of Splines on Triangulated Quadrangulations (with M.-J. Lai), SIAM J. Numer. Anal. 36 (1999), 143--159. (Click for ps)

  2000

• Non-Existence of Star-Supported Spline Bases (with P. Alfeld), SIAM J. Math. Anal. 31 (2000), 1482--1501. (Click for ps)
• A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere (with T. Lyche), SIAM J. Sci. Comp. 22 (2000), 724--74746. (Click for ps)
• Stable local nodal bases for C^1 bivariate polynomial splines, (with Oleg Davydov), in Curve and Surface Fitting: Saint-Malo 99, A. Cohen, C. Rabut, and L. Schumaker (eds), Vanderbilt University Press, 2000, 171--180. (click for ps)
• Locally linearly independent bases for bivariate polynomial spline spaces ( with Oleg Davydov), Adv. Comp. Math. 13 (2000), 355--373. (Click for ps)

  2001

• Local Lagrange interpolation by bivariate C^1 cubic splines, (with Guenther Nurnberger and Frank Zeilfelder), Mathematical Methods in CAGD: Oslo 2000, Tom Lyche and Larry Schumaker (eds.), Vanderbilt University Press, 2001, 393--404. (click for ps)
• Macro-elements and stable local bases for splines on Clough-Tocher triangulations (with Ming-Jun Lai), Numer. Math. 88 (2001), 105--119. (Click for ps)
• On stable local bases for bivariate polynomial spline spaces, (with Oleg Davydov), Constructive Approx. 18 (2001), 87--116. (click for ps)

  2002

• Smooth macro-elements based on Clough-Tocher triangle splits, (with P. Alfeld), Numer. Math. 90 (2002), 597--616. (click for ps)
• Smooth Macro-elements based on Powell-Sabin triangle splits, (with P. Alfeld), Advances in Comp. Math. 16 (2002), 29--46. (click for ps)
• Approximation and interpolation with C^1 quartic bivariate splines, (with O. Davydov), SIAM J. Numer. Anal. 39 (2002), 1732--1748. (click for ps)
• Bounds on projections onto bivariate polynomial spline spaces with stable bases, (with Manfred von Golitschek, Constructive Approx. 18 (2002), 241--254. (click for ps)
• Quadrilateral macro-elements, (with M.-J. Lai), SIAM J. Math. Anal. 33 (2002), 1107--1116. (click for ps)

  TO APPEAR

• Macro-elements and stable local bases for splines on Powell-Sabin triangulations (with Ming-Jun Lai), Math. Comp., to appear. (Click for ps)
• Error bounds for minimal energy bivariate polynomial splines, (with Manfred von Golitschek and Ming-Jun Lai), Numer. Math. To appear. (click for ps)
• On the approximation order of splines on spherical triangulations, (with Mike Neamtu), Adv. in Comp. Math. To appear. (click for ps)

  SUBMITTED

• Upper and lower bounds on the dimension of superspline spaces, (with Peter Alfeld). (click for ps)
• Lagrange interpolation by $C^1$ cubic splines on triangulated quadrangulations, with G. Nurnberger and F. Zeilfelder. (click for ps)

Tex Macros

• at98.unix. This file contains the TEX macros for the Approximation IX Proceedings. It is designed for UNIX users. The necessary files are tarred and compressed. Save the file as "at98.unix", and then type "sh at98.unix".
• at98.pc. This file contains the TEX macros for the Approximation IX Proceedings. It is designed for PC and Mac users. The necessary files are strung together, one after the other. To separate them, use an editor to find END, and cut out the individual files listed in README.

Editorial Boards of Journals

• Advances in Computational Mathematics
• Computer-Aided Geometric Design
• Constructive Approximation

Series Editor

• Innovations in Applied Mathematics. This is a book series published by Vanderbilt University Press.
  

Spline Bibliography

• Access to the deBoor/Schumaker bibliography of splines.

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