Larry L. Schumaker

Stevenson Professor of Mathematics
Office: Stevenson Center 1532
Phone: (615) 322-6652
EMAIL: larry.schumaker (at) vanderbilt.edu

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Vita

Full vita.

Publications

Spline Books

Spline Bibliographies

Access Supplemental bibliography for Splines on Triangulations.
Access Supplemental bibliography for Spline Functions: Computational Methods.
Access to the deBoor/Schumaker bibliography of splines.

Spline Software

SPLINEPAK Matlab package for the book Spline Functions: Computational Methods)

Current Conference Organization

Recent Conference Organization

Curves and Surfaces , Avignon, June 29 -- July 5, 2006.
Twelfth International Conference on Approximation Theory. San Antonio, March 4--8, 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.
Fifthteenth International Conference on Approximation Theory San Antonio, Texas, May 22--25, 2016.
Ninth International Conference on Mathematical Methods for Curves and Surfaces Tonsberg, Norway, June 23 -- June 28, 2016.
Ninth Itnternational Conference on Curves and Surfaces, Archachon, France, June 24 -- Juy 4, 2018.
Sixteenth International Conference on Approximation Theory Nashville, TN, May 19 -- 22, 2019.

Related Conferences

IGA 2018: Integrating Design and Analysis. Austin, Texas, Oct. 10-12, 2018.
SIAM Computational Geometry, Vancouver, June 17--19, 2019.
Multivariate Approximation and Interpolation with Applications Vienna, 26--30 August, 2019.

Genealogy

Advisor Tree

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 surface fitting on surfaces using projected Powell-Sabin splines (with Oleg Davydov), in Mathematics of Surfaces 2007, R. Martin, M. Sabin, and J. Winkler (eds.), Springer, 2007, 138--153.
2008
Interpolation and scattered data fitting on manifolds using projected Powell-Sabin splines (with Oleg Davydov), \IMAJNA (2008), 785--05.
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), 1017--1036.
Bounds on the dimension of trivariate spline spaces (with Peter Alfeld), Advances in Comp. Math. 29 (2008), 315--335.
Computing bivariate splines in scattered data fitting and the finite-element method, Numerical Algorithms 48 (2008), 237--260.
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(), 89--102.
A $C^1$ quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions (with Tatyana Sorokina and Andrew J. Worsey), J. Approx. Th. 158 (2009), 126--260.
A domain decomposition method for computing bivariate spline fits of scattered data (with M.-J. Lai), SIAM J. Numer. Anal. 47 (2009), 911--928.
2010
Two condensed macro-elements with full approximation power, (with P. Alfeld and T. Sorokina), Adv. in Comp. Math. 32 (2010), 381--391.
Nonnegativity preserving macro-element interpolation of scattered data, (with H. Speleers), CAGD 27 (2010), 245--261.
2011
Spline spaces on TR-meshes with hanging vertices, with Lujun Wang, Numer. Math. 118 (2011), 531--548. Contact me for a reprint.
Convexity preserving splines over triangulations, with H. Speleers, CAGD 28 (2011), 270--284. Contact me for a reprint.
2012
Splines on triangulations with hanging vertices, with Lujun Wang, Constructive Approximation~36 (2012), 487--511. Contact me for a reprint.
Approximation power of polynomial splines on T-meshes, with Lujun Wang, Computer Aided Geometric Design 29 (2012), 599--612. Contact me for a reprint.
2013
On Hermite interpolation with polynomial splines on T-meshes, with Lujun Wang, Journal of Computational and Applied Mathematics 240 (2013), 42--50. Contact me for a reprint.
Splines on spherical triangulations with hanging vertices, Computer Aided Geometric Deisgn 30 (2013), 263--275. Contact me for a reprint.
2014
Convexity preserving $C^0$ splines, with H. Speleers, \AiCM 40 (2014), 117--135. Contact me for a preprint.
2016
Bernstein-B\'ezier finite elements on tetrahedral-hexahedral-pyramidal partitions , with M. Ainsworth and O. Davydov, Comp. Methods in Appl. Mech. and Engr. 304 (2016), 140--170;
2017
Adaptive computation with splines on triangulations with hanging vertices , with Shiying Li, Approximation Theory XV: San Antonio 2016, Springer Proc. Math. 201, G. E. Fasshauer and Larry L. Schumaker, eds., (2017), 197--218.
2019
Solving Elliptic PDE's on Domains with Curved Boundaries with an Immersed Penalized Boundary Method, J Sci Comp. {\bf 80(3)} (2019), 1369--1394.
2020
Approximation by Polynomial Splines on Curved Triangulations, submitted.

Editorial Boards of Journals

Series Editor

Innovations in Applied Mathematics. This is a book series published by Vanderbilt University Press.
Modern Methods in Applied Mathematics. This is a book series published by Nashboro Press.

Larry L. Schumaker

Vita

Publications

Spline Books

Spline Bibliographies

Spline Software

Current Conference Organization

Recent Conference Organization

Related Conferences

Genealogy

Research Interests

Recent Papers

Editorial Boards of Journals

Series Editor

Library and Math Resources