Larry L. Schumaker

Vita

• Full vita.

Publications

• Complete List of Research Papers
• Complete List of Books

Spline Books

• Spline Functions: Basic Theory
• Spline Functions on Triangulations
• Spline Functions: Computational Methods

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

• 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.
  
• Modern Methods in Applied Mathematics. This is a book series published by Nashboro Press.
  

Library and Math Resources

• Library
  
• Electronic Journals
  
• SIAM Pubs
• CML Membership
• MathSciNet
• VU Press
• NSF Fastlane
• Math Dept