Larry L. Schumaker
Stevenson Professor of Mathematics
Office: Stevenson Center 1532
Phone: (615) 3226652
Email: larry.schumaker at) vanderbilt.edu
Course Pages
Spline Books
Spline Bibliographies

Access A bibliography of multivariate splines.

Access to the deBoor/Schumaker bibliography of splines.
Current Conference Organization
Recent Conference Organization

Curves and Surfaces , Avignon, June 29  July 5, 2006.

Twelfth International Conference on Approximation Theory.
San Antonio, March 48, 2007.

Seventh International
Conference on Mathematical Methods for Curves and Surfaces
Tonsberg, Norway, June 26  July 1, 2008.

Thirteenth International
Conference on Approximation Theory,
San Antonio, March 7  March 10, 2010.

Curves and Surfaces , Avignon, June 24  June 30, 2010.

Eighth International
Conference on Mathematical Methods for Curves and Surfaces
Oslo, Norway, June 28  July 3, 2012.

Fourteenth International
Conference on Approximation Theory
San Antonio, Texas, April 7  10, 2013.

Eighth International
Conference on Curves and Surfaces,
Paris, France, June 12  18, 2014.
Related Conferences

23rd Biennial Conference on Numerical Analysis,
Glasgow, June 2326, 2009.

Approximation and Operator Theory III, Volyn, Ukrain, Aug. 2226, 2009.

Algorithms for Approximation VI, , Ambleside, England, Aug. 31  Sept. 4, 2009.

SIAM Geometric and Physical Modeling,
San Francisco, Oct. 58, 2009.

Applied Mathematics and Scientific Computing,
Zagreb, Sept. 14  18, 2009.

Multivariate approximation and interpolation with applications,
Edinburgh, Sept. 610, 2010.

Approximation Theory, Nashville, May 1721, 2011.
 Applied Math and Scientific Computing,
Trogir, Croatia, June 1317, 2011.

Multivariate Approximation: Theory and Applications,
Priapolis, Uruguary, August 13  19, 2011.

SIAM Geometric Modeling,
Orlando, Oct. 2427, 2011.

International Symposium on Approximation Theory,
Nashville, TN, May 1721, 2011.

New Trends in Approximation Theory,
Eid Gedi, Israel, Jan. 47, 2012.

Jaen Conference on Approximation Theory,
Ubeda, Spain, July 1520, 2012.

Inverse Problems and PDE's,
Orlando, May 9  11, 2013.

11th Conference on Approximation and Optimization in the Caribbean,
Puebla, Mexico, October 8  13, 2013.
Vitas
Publications
Genealogy
Research Interests
 Approximation Theory (Splines)
 CAGD
 Numerical Analysis
Recent Papers
1995:
 Circular BernsteinBezier 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), 405424.
1996:

Multipatch parametric surfaces with minimal energy,
with Greg Fasshauer, Comp. Aided. Geom. Design {\bf 13} (1996), 4579.
 BernsteinBezier Polynomials on Spheres and
SphereLike Surfaces
(with Peter Alfeld and Mike Neamtu), CAGD 13 (1996), 333349.
 Dimension and Local Bases of Homogeneous Spline
Spaces (with Peter Alfeld and Mike Neamtu), SIAM J. Math.
Anal. 27 (1996), 14821501.
 Fitting scattered data on spherelike
surfaces using spherical splines (with P. Alfeld and M. Neamtu),
J. Comp. Appl. Math. 73 (1996), 543.
 Hybrid Bezier Patches on SphereLike Surfaces
(with Xiaoyu Liu), J. Comp. Appl. Math. 73 (1996), 157172.
 Shapepreserving Knot Removal
(with S. Stanley),
Comp. Aided Geom. Design {\bf 13} (1996), 851872.

Total positivity properties of LBsplines, with Tom Lyche,
in Total Positivity and Its Applications,
M. Gasca and C. Micchelli (eds.), Kluwer, Dordrecht, 1996, 3546.
1997
 Scattered Data Interpolation Using
C^2 Supersplines of Degree Six
(with M.J. Lai) SIAM J. Numer. Anal. 34 (1997), 905921.

Fitting monotone surfaces to scattered data using $C^1$
piecewise cubics, with Lu Han, SIAM J. Numer. Anal. {\bf 34} (1997),
569585.
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, 117166.
 Designing NURBS Cam Profiles
using Trigonometric Splines
(with M. Neamtu and H. Pottmann), ASME J. Mech. Design. {\bf 120}
(1998), 175180.
 Quasiinterpolants Based on Trigonometric
Splines
(with S. Stanley and T. Lyche), J. Approx. Th. 95 (1998), 280309.
 On the Approximation Power of Bivariate
Splines
(with M.J. Lai), Adv. in Comp. Math. 9 (1998), 251279.
1999
 Dual Focal Splines and Rational Curves
with Rational Offsets
(with M. Neamtu and H. Pottmann), Mathematical Engineering in Industry
7 (1999), 139154.
 On the Approximation Power of Splines
on Triangulated Quadrangulations
(with M.J. Lai), SIAM J. Numer. Anal. 36 (1999), 143159.
2000
 NonExistence of StarSupported Spline
Bases (with P. Alfeld), SIAM J. Math. Anal. 31 (2000), 14821501.
 A Multiresolution Tensor Spline Method
for Fitting Functions on the Sphere (with T. Lyche), SIAM J. Sci.
Comp. 22 (2000), 72474746.
 Stable local nodal bases for C^1 bivariate
polynomial splines, (with Oleg Davydov), in
Curve and Surface Fitting: SaintMalo 99, A. Cohen, C. Rabut, and L.
Schumaker (eds), Vanderbilt University Press, 2000, 171180.
 Locally linearly independent bases for
bivariate polynomial spline spaces ( with Oleg Davydov),
Adv. Comp. Math. 13 (2000), 355373.
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, 393404.
 Macroelements and stable local bases for
splines on CloughTocher triangulations (with MingJun Lai),
Numer. Math. 88 (2001), 105119.
 On stable local bases for bivariate
polynomial spline spaces, (with Oleg Davydov), Constructive
Approx. 18 (2001), 87116.
2002
 Bounds on projections onto bivariate polynomial
spline spaces with stable bases, (with Manfred von Golitschek,
Constructive Approx. 18 (2002), 241254.
 Smooth macroelements based on
CloughTocher triangle splits, (with P. Alfeld), Numer. Math.
90 (2002), 597616.
 Quadrilateral macroelements,
(with M.J. Lai), SIAM J. Math. Anal. 33 (2002), 11071116.
 Stable approximation and interpolation with C^1
quartic bivariate splines, (with O. Davydov), SIAM J. Numer.
Anal. 39 (2002), 17321748.
 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, 405424.
 Smooth Macroelements based on
PowellSabin triangle splits, (with P. Alfeld),
Advances in Comp. Math. 16 (2002), 2946.
 Error bounds for minimal energy bivariate
polynomial splines,
(with Manfred von Golitschek and MingJun Lai),
Numer. Math. 93 (2002), 315331.
 Penalized least squares fitting,
(with Manfred von Golitschek),
Serdica 18 (2002), 10011020.
2003
 Upper and lower bounds on the dimension
of superspline spaces, (with Peter Alfeld),
Constructive Approx. 19 (2003), 145161.
 Macroelements and stable local bases for
splines on PowellSabin triangulations (with MingJun Lai),
Math. Comp. 72 (2003), 335354.
 Approximating weak Chebyshev subspaces
by Chebyshev subspaces,
(with F. Deutsch and Z. Ziegler), J. Approx. Th. 123 (2003),
188213.
2004
 On the approximation order of splines
on spherical triangulations, (with Mike Neamtu),
Adv. in Comp. Math. 21 (2004), 320.
 Lagrange interpolation by $C^1$ cubic
splines on triangulated quadrangulations,
(with G. Nurnberger and F. Zeilfelder),
Adv. in Comp. Math. 21 (2004), 357380.
 $C^1$ quintic splines on type4 tetrahedral
partitions,
(with Tatyana Sorokina), Adv. in Comp. Math. 21 (2004), 421444.

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,
345370.

Surface compression using a space of C^1 splines,
(with Don Hong), Computing 72 (2004), 7992.

Multisided macroelement spaces based on CloughTocher
triangle splits,
(with Vera Rayevskaya), CAGD 22 (2004), 5779.
2005
 A trivariate box macroelement,
(with Tatyana Sorokina), Constr. Approx. 21 (2005), 413431.

A C^2 trivariate doubleCloughTocher macroelement,
(with Peter Alfeld), in Approximation Theory XI: Gatlinburg 2004,
C. Chui, M. Neamtu, and L. L. Schumaker (eds), Nashboro Press
(Brentwood), 2005, 114.

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, 327344.

A C^2 trivariate macroElement based on the
CloughTocher split of a tetrahedron,
(with Peter Alfeld), Comp. Aided Geom. Design 22 (2005), 710721.
 A C^2 trivariate macroelement based on
the WorseyFarinsplit of a tetrahedron (with
P. Alfeld), SIAM J. Num. Anal. 43 (2005), 17501765.
2006
 Local Lagrange interpolation with bivariate
splines of arbitrary smoothness (with
G. Nurnberger, V. Rayevskaya, and F. Zeilfelder), Constr. Approx. 23 (2006), 3359.

A family of $C^r$ Macroelements on PowellSabin12 splits,
(with Tanya Sorokina), Math. Comp. 75 (2006), 711726.
2007

Trivariate $C^r$ polynomial macroelements
(with MingJun Lai), Constr. Approx. 26 (2007), 1128.

Scattered surface fitting on
surfaces using projected PowellSabin splines (with Oleg Davydov),
in Mathematics of Surfaces 2007, R. Martin, M. Sabin, and J. Winkler
(eds.), Springer, 2007, 138153.
2008

Interpolation and scattered data fitting on
manifolds
using projected PowellSabin splines (with Oleg Davydov),
\IMAJNA (2008), 78505.

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. 77 (2008), 10171036.

Bounds on the dimension of trivariate spline spaces
(with Peter Alfeld), Advances in Comp. Math.
29 (2008), 315335.

Computing bivariate splines in scattered
data fitting and the finiteelement method,
Numerical Algorithms 48 (2008), 237260.
2009

Local Lagrange interpolation with cubic $C^1$
splines on tetrahedral partitions (with G. Hecklin,
G. Nurnberger, and F. Zeilfelder),
J. Approx. Th. 160 (200(), 89102.

A $C^1$ quadratic trivariate macroelement space
defined over arbitrary tetrahedral partitions (with
Tatyana Sorokina and Andrew J. Worsey),
J. Approx. Th. 158 (2009), 126260.

A domain decomposition method for computing bivariate spline fits
of scattered data (with M.J. Lai), SIAM J. Numer. Anal.
47 (2009), 911928.
2010

Two condensed macroelements with full approximation power,
(with P. Alfeld and T. Sorokina), Adv. in Comp. Math. 32 (2010), 381391.

Nonnegativity preserving macroelement
interpolation of scattered data, (with H. Speleers),
CAGD 27 (2010), 245261.
2011
 Spline spaces on TRmeshes with hanging vertices,
with Lujun Wang, Numer. Math. 118 (2011), 531548. Contact me for a reprint.
 Convexity preserving splines over triangulations,
with H. Speleers, CAGD 28 (2011), 270284. Contact me for a reprint.
2012
 Splines on triangulations with hanging vertices, with
Lujun Wang, Constructive Approximation, to appear. Contact me for a preprint.
 Convexity preserving $C^0$ splines, with H. Speleers, submitted.
 Approximation power of polynomial splines on Tmeshes,
with Lujun Wang, submitted.
 On Hermite interpolation with
polynomial splines on Tmeshes, with Lujun Wang,
submitted.
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