Larry L. Schumaker
Stevenson Professor of Mathematics
Office: Stevenson Center 1532
Phone: (615) 322-6652
Email: larry.schumaker at) vanderbilt.edu
Spline Books
Spline Bibliographies
-
Access A bibliography of multivariate splines.
-
Access to the deBoor/Schumaker bibliography of splines.
Current Conference Organization
Recent Conference Organization
-
Eleventh International Conference on Approximation Theory.
Gatlinburg, TN, May 18--22, 2004.
-
CAGD Workhop,
Bergen-Tromso, Norway, June 24--30, 2004.
-
Mathematical Methods for Curves and Surfaces.
Tromsoe, Norway, July 1--6, 2004.
-
FOCM05 CAGD Workshop.
Santander, Spain, July, 2005.
-
Curves and Surfaces , Avignon, June 29 -- July 5, 2006.
-
Twelfth International Conference on Approximation Theory.
San Antonio, March 4--8, 2007.
Related Conferences
-
MAIA 2004 Hohenheim, Germany, October 13--17, 2004.
-
Wavelets and Splines Athens, GA, May 16--19, 2005.
-
Algorithms for Approximation V Chester, England,
July 18 -- 22, 2005.
-
Multivariate Approximation Bommerholz, Germany,
Sept. 25-- Oct. 1, 2005.
-
SIAM Geometric Design, Phoenix, Oct. 30 -- Nov. 3, 2005.
-
Multivariate Approximation , Cancun, April 26 -- May 1, 2007.
-
SIAM CAGD Conference.
San Antonio, Nov. 4 -- 8, 2007.
Short Vita
Publications
Genealogy
Research Interests
- Approximation Theory (Splines)
- CAGD
- Numerical Analysis
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
- 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.
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.
- Dimension and Local Bases of Homogeneous Spline
Spaces (with Peter Alfeld and Mike Neamtu), SIAM J. Math.
Anal. 27 (1996), 1482--1501.
- Fitting scattered data on sphere-like
surfaces using spherical splines (with P. Alfeld and M. Neamtu),
J. Comp. Appl. Math. 73 (1996), 5--43.
- Hybrid Bezier Patches on Sphere-Like Surfaces
(with Xiaoyu Liu), J. Comp. Appl. Math. 73 (1996), 157--172.
- Shape-preserving Knot Removal
(with S. Stanley),
Comp. Aided Geom. Design {\bf 13} (1996), 851--872.
-
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.
-
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.
- Designing NURBS Cam Profiles
using Trigonometric Splines
(with M. Neamtu and H. Pottmann), ASME J. Mech. Design. {\bf 120}
(1998), 175--180.
- Quasi-interpolants Based on Trigonometric
Splines
(with S. Stanley and T. Lyche), J. Approx. Th. 95 (1998), 280--309.
- On the Approximation Power of Bivariate
Splines
(with M.-J. Lai), Adv. in Comp. Math. 9 (1998), 251--279.
1999
- Dual Focal Splines and Rational Curves
with Rational Offsets
(with M. Neamtu and H. Pottmann), Mathematical Engineering in Industry
7 (1999), 139--154.
- On the Approximation Power of Splines
on Triangulated Quadrangulations
(with M.-J. Lai), SIAM J. Numer. Anal. 36 (1999), 143--159.
2000
- Non-Existence of Star-Supported Spline
Bases (with P. Alfeld), SIAM J. Math. Anal. 31 (2000), 1482--1501.
- A Multiresolution Tensor Spline Method
for Fitting Functions on the Sphere (with T. Lyche), SIAM J. Sci.
Comp. 22 (2000), 724--74746.
- 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.
- Locally linearly independent bases for
bivariate polynomial spline spaces ( with Oleg Davydov),
Adv. Comp. Math. 13 (2000), 355--373.
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.
- Macro-elements and stable local bases for
splines on Clough-Tocher triangulations (with Ming-Jun Lai),
Numer. Math. 88 (2001), 105--119.
- On stable local bases for bivariate
polynomial spline spaces, (with Oleg Davydov), Constructive
Approx. 18 (2001), 87--116.
2002
- Bounds on projections onto bivariate polynomial
spline spaces with stable bases, (with Manfred von Golitschek,
Constructive Approx. 18 (2002), 241--254.
- Smooth macro-elements based on
Clough-Tocher triangle splits, (with P. Alfeld), Numer. Math.
90 (2002), 597--616.
- Quadrilateral macro-elements,
(with M.-J. Lai), SIAM J. Math. Anal. 33 (2002), 1107--1116.
- Stable approximation and interpolation with C^1
quartic bivariate splines, (with O. Davydov), SIAM J. Numer.
Anal. 39 (2002), 1732--1748.
- Local Lagrange interpolation by $C^1$ cubic splines
on triangulations of separable quadrangulations,
(with G. Nurnberger and F. Zeilfelder,
in Approximation Theory X: Splines, Wavelets,
and Applications,
Charles K. Chui and Larry L. Schumaker (eds.),
Vanderbilt University Press, Nashville, 2002, 405--424.
- Smooth Macro-elements based on
Powell-Sabin triangle splits, (with P. Alfeld),
Advances in Comp. Math. 16 (2002), 29--46.
- Error bounds for minimal energy bivariate
polynomial splines,
(with Manfred von Golitschek and Ming-Jun Lai),
Numer. Math. 93 (2002), 315--331.
- Penalized least squares fitting,
(with Manfred von Golitschek),
Serdica 18 (2002), 1001--1020.
2003
- Upper and lower bounds on the dimension
of superspline spaces, (with Peter Alfeld),
Constructive Approx. 19 (2003), 145--161.
- Macro-elements and stable local bases for
splines on Powell-Sabin triangulations (with Ming-Jun Lai),
Math. Comp. 72 (2003), 335-354.
- Approximating weak Chebyshev subspaces
by Chebyshev subspaces,
(with F. Deutsch and Z. Ziegler), J. Approx. Th. 123 (2003),
188--213.
2004
- On the approximation order of splines
on spherical triangulations, (with Mike Neamtu),
Adv. in Comp. Math. 21 (2004), 3--20.
- Lagrange interpolation by $C^1$ cubic
splines on triangulated quadrangulations,
(with G. Nurnberger and F. Zeilfelder),
Adv. in Comp. Math. 21 (2004), 357--380.
- $C^1$ quintic splines on type-4 tetrahedral
partitions,
(with Tatyana Sorokina), Adv. in Comp. Math. 21 (2004), 421--444.
-
Local Lagrange interpolation with $C^2$ splines
of degree seven on triangulations,
with G. N\"urnberger, V. Rayevskaya, and F. Zeilfelder,
in {\sl Advances in Constructive Approximation: Vanderbilt 2003},
Mike Neamtu and Ed Saff (eds.), Nashboro Press, Brentwood, 2004,
345--370.
-
Surface compression using a space of C^1 splines,
(with Don Hong), Computing 72 (2004), 79--92.
-
Multi-sided macro-element spaces based on Clough-Tocher
triangle splits,
(with Vera Rayevskaya), CAGD 22 (2004), 57--79.
2005
- A trivariate box macro-element,
(with Tatyana Sorokina), Constr. Approx. 21 (2005), 413--431.
-
A C^2 trivariate double-Clough-Tocher macro-element,
(with Peter Alfeld), in Approximation Theory XI: Gatlinburg 2004,
C. Chui, M. Neamtu, and L. L. Schumaker (eds), Nashboro Press
(Brentwood), 2005, 1--14.
-
Two Lagrange interpolation methods
based on $C^1$ splines on tetrahedral partitions,
(with G. N\"urnberger and F. Zeilfelder),
in Approximation Theory XI: Gatlinburg 2004,
C. Chui, M. Neamtu, and L. L. Schumaker (eds), Nashboro Press
(Brentwood), 2005, 327--344.
-
A C^2 trivariate macro-Element based on the
Clough-Tocher split of a tetrahedron,
(with Peter Alfeld), Comp. Aided Geom. Design 22 (2005), 710-721.
- A C^2 trivariate macro-element based on
the Worsey-Farin-split of a tetrahedron (with
P. Alfeld), SIAM J. Num. Anal. 43 (2005), 1750--1765.
2006
- Local Lagrange interpolation with bivariate
splines of arbitrary smoothness (with
G. Nurnberger, V. Rayevskaya, and F. Zeilfelder), Constr. Approx. 23 (2006), 33-59.
-
A family of $C^r$ Macro-elements on Powell-Sabin-12 splits,
(with Tanya Sorokina), Math. Comp. 75 (2006), 711-726.
2007
-
Trivariate $C^r$ polynomial macro-elements
(with Ming-Jun Lai), Constr. Approx. 26 (2007), 11--28.
-
Scattered data fitting on surfaces using projected Powell-Sabin splines
(with Oleg Davydov), in Mathematics of Surfaces 2007, R. Matin, M. Sabin, and
J. Winkler (eds.), Springer, 2007, 138--153.
-
Interpolation and scattered data fitting on manifolds
using projected Powell-Sabin splines
(with Oleg Davydov), IMA J. Numer. Anal., 2007, DOI: drm033v1-drm033.
-
A local Lagrange interpolation method based on $C^1$ cubic
splines on Freudenthal partitions (with G. Hecklin,
G. N\"urnberger, and F. Zeilfelder), Math. Comp., DOI: 10.1090/S0025-5718-07-02056-X.
-
Bounds on the dimension of trivariate spline spaces
(with Peter Alfeld), Advances in Comp. Math., DOI: 10.1007/s10444-007-9051-6.
TO APPEAR
-
Computing bivariate splines in scattered data fitting and the finite-element
method , Numer. Algs., to appear.
-
A C^1 quadratic trivariate macro-element space defined over arbitrary
tetrahedral paritions, (with T. Sorokina and A. Worsey), to appear.
-
Local Lagrange interpolation with cubic C^1 splines on tetrahedral partitions
with G. Hecklin, G. Nurnberger, and F. Zeilfelder),
to appear.
Editorial Boards of Journals
Series Editor
Library and Math Resources