Tom Lyche

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Academic Interests

  • Approximation Theory 
  • Numerical Analysis
  • Spline Theory
  • Isogeometric Analysis
New book: Tom Lyche and Jean-Louis Merrien, Exercises in Computational Mathematics with MATLAB, 372pp, Springer 2014


Higher education and employment history


1975  Ph.D., Mathematics, Dep. of Mathematics, Univ. of Texas, Austin, USA.

1969 Cand. real (M.Sc.) Mathematics, Dept. of Mathematics, Univ. of Oslo.

1967 Cand. mag., (B.Sc)  Univ. of Oslo.

Employment history

 2014-current       Professor emeritus, Dep. of Mathematics, Univ. of Oslo

1984 – 2013        Professor, Dep. of Informatics, Univ. of Oslo 

1977 –1984         Associate Professor (Dosent) Dep. of Informatics, Univ. of Oslo

1976                    Associate Professor (Dosent) Dep of Mathematics, Univ. of Oslo

1972-1976           Assistant Professor (Universitetslektor), Mathematics, Univ. of Oslo

2003-current        Member CMA, Centre of Mathematics for Applications

1993 -current        Consultant, SINTEF Oslo.


  • The Dagstuhl foundation’s John Gregory Memorial Award for "Outstanding contributions to geometric modeling", 2003.
  • Elected member of the Norwegian Academy of Science and Letters in 2000.


  • Leader of the Mathematics group, the Norwegian Academy of Science and Letters 2005 - 2013.
  • Member of the Selection Committee for SIAM’s Polya Prize 2010
  • Member of the board of the Nordic Foundation for the Journal BIT, 2004-current, appointed by the Norwegian Academy of Science and Letters.


Visiting positions of 5-12 Month Duration

Sept 2007-July 2008           Visiting Professor, University of Utah, USA

Jan. 1998 – June 1998        Visiting Professor, Paul Sabatier University and I.N.S.A.Toulouse, France

Aug. 1993 – June 1994       Visiting Professor, Rice University, USA

Mars – Aug. 1987          Visiting Professor, Univ of Utah, USA

Jan-Dec. 1983                Visiting Associate Professor, Texas A&M Univ, USA

Aug – Dec. 1973,                Visiting Assistant Professor, Math. Res. Center,Univ. of Wisconsin, USA

Invited,  Shorter Visits

June 2006                       Universita di Roma “Tor Vergata”

April 2005                       Univ. di Roma “Tor Vergata” and Univ. di Sienna

June 2003                      University of Rennes, France

April 2002                      Universita degli Studi di Sienna.

April-May 2000             Univ. of Grenoble, France

June-Aug. 1983             Univ. of Utah, USA

June-Aug 1974               Math. Res. Center, Univ. of Wisconsin, USA         



  • Lyche, T. and G. Muntingh, Stable Simplex Spline Bases for $C^3$ Quintics on the Powell--Sabin 12-Split,  Constr Approx 45 (2017) 1--32. doi:10.1007/s00365-016-9332-8.
  • Bracco,  C., Lyche, T., Manni, C., Roman, F. and Speleers, H., On the dimension of Tchebycheffian spline spaces over planar T-meshes, \CAGD 45 (2016), 151--173.
  • Cesare Bracco , Tom Lyche, Carla Manni, Fabio Roman, Hendrik SpeleersGeneralized spline spaces over T-meshes: dimension formula and locally refined generalized B-splines, Applied Mathematics and Computation, 272 (2016), 187--198. 
  • Lyche, T. and G. Muntingh, A Hermite interpolatory subdivision scheme for C2-quintics on the Powell--Sabin 12-split, Computer Aided Geometric Design, 31 (2014), 464--474.
  • ​Dokken, T., T.  Lyche, and K. F. Pettersen, Polynomial splines over locally refined box-partitions, Computer Aided Geometric Design, 30 (2013), 331--356.
  • Cohen, E., T.~Lyche, and R. F. Riesenfeld, A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines, Mathematics of Computation, 82 (2013), 1667--1707.

  • Lyche, T. and M-L Mazure, Piecewise Chebyshevian multiresolution analysis,  East Journal of  Approximation 17 (2011), 410--426.

  • Cohen, E., Martin, T., Kirby, R.M., Lyche, T, and R.F. Riesenfeld, Analysis-aware modelling: Understanding quality considererations in modeling for isogeometric analysis, Comp. Methods Appl. Mech. Engrg, 199 (2010), 334--356.

  • ​Cohen, E., T.~Lyche, and R.~F.~Riesenfeld, MCAD: Key Historical Developments, Comp. Methods Appl. Mech. Engrg,  199 (2010), 224--228.

  • Lyche, T, K. Mørken, and F Pelosi, Stable, linear spline wavelets on nonuniform knots with vanishing moment's, Computer Aided Geometric Design, 26 (2009), 203--216.

  • Floater, M and T. Lyche, Divided differences of inverse functions and partitions of a convex polygon, Mathematics of Computation, 77 (2008), 2295--2308.

  • Lyche, T., C. Manni, and  P. Sablonnière, Quasi-interpolation projectors for Box Splines, Journal of Computational and Applied Mathematics, 221 (2008),416--429.

  • Floater, M and T. Lyche, Two Chain Rules for Divided Differences and Faà di Bruno’s Formula, Mathematics of Computation, 76 (2007), 867 – 877.

  • Lyche, T. and J-L. Merrien, Hermite subdivision with shape constraints on a rectangular mesh, BIT, 46 (2006), 831--859.

  • Lyche, T. and K. Scherer, Mixed norm condition numbers for the univariate Bernstein basis, Banach Center Publications, 72 ( 2006), 177 – 188.

  • Lyche, T. and K. Scherer, Addendum to ”On the L1-Condition Number of the Univariate Bernstein Basis”, Constructive Approximation, 24 (2006), 239 – 243.

  • Lyche, T. and J-L Merien, C1 Interpolatory Subdivision with Shape Constraints for Curves, Siam J. Numer. Anal., 44 (2006), 1095 – 1121.

  • Lyche, T and M-L Mazure, On the Existence of Piecewise Exponential B-splines, Advances in Computational Mathematics, 25 (2006), 105  - 133.

  • Costantini, P., Lyche,T., and Manni,C., On a Class of Weak Tchebycheff Systems, Numerische Mathematik, 101 (2005),333-354.

  • Sederberg, T., Cardon, D.L., Finnigan, G. T., Zheng, J., and Lyche, T., T-spline Simplification ans Local Refinement, ACM Transactions on Graphics(TOG),  23 (2004),276-283.

  • Lyche, T and J. M. Peña, Optimally Stable Multivariate Bases, Advances in Computational Mathematics, 20 (2004), 149 - 159.

  • Lyche, T. and K. Scherer, On the L1-condition number of the univariate Bernstein basis, Constructive Approximation, 18 (2002),503 - 528.

  •  Lyche, T. K. Nilssen,and R. Winther, Preconditioned Iterative Methods for Scattered Data Interpolation, Advances in Computational Mathematics, 17 (2002), 237 - 256.

  • Byung-Gook Lee, Tom Lyche, and Knut Mørken, Some Examples of Quasi-Interpolants Constructed from Local Spline Projectors, in Mathematical Methods for curves and surfaces, Oslo 2000, T. Lyche and L. L. Schumaker (eds.), Vanderbilt University Press, 2001, 243-252.

  • Lyche, T., Mørken, K., and E. Quak, Theory and Algorithms for non-uniform spline wavelets, in Multivariate Approximation and Applications, N. Dyn, D. Leviatan, D. Levin, and A. Pinkus,(eds), Cambridge University Press, 2001, 152-187.

  • Lyche, T. and L. L. Schumaker, A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere, SIAM Journal of Scientific Computing, 22 (2000), 724-746.

  • Lyche, T. and K. Scherer, On the p-norm Condition Number of the Multivariate Triangular Bernstein Basis, Journal of Computational and Applied Mathematics, 119 (2000), 259-273.

  •  Dæhlen, M., T. Lyche, K. Mørken, R. Schneider, and H-P. Seidel, Multiresolution analysis based on quadratic Hermite interpolation on triangles, Journal of Computational and Applied Mathematics, 119 (2000), 97--114.

  • Floater, M. and Lyche, T., Asymptotic Convergence of Degree-Raising, Advances in Computational Mathematics 12 (2000), 175-187.

  •  Stark, M. M., Cohen, E., Lyche, T., and R. F. Riesenfeld, Computing exact shadow irradiance using splines, Siggraph Computer Graphics Proceedings, Annual Conference Series, 1999,155 -- 164.

  • Lyche, T. and K. Mørken, The sensitivity of spline functions to perturbations of the knots, BIT 39 (1999), 305-322. 

  • Lyche, T., Trigonometric Splines; a survey with new results, in Shape Preserving Representations in Computer Aided Geometric Design,
    J. M. Peña (ed), Nova Science Publishers, Inc., New York, 1999, 201-- 227.

  • Dyn, N. and T. Lyche, A Hermite subdivision scheme for the evaluation of the Powell-Sabin 12-split element, in Approximation Theory IX, Volume 2, Charles Chui and Larry L. Schumaker (eds.) Vanderbilt University Press, Nashville,33-38, 1998.

  •  Lyche, T., L. L. Schumaker, and S. Stanley, Quasi-interpolants Based on Trigonometric Splines, J. Approximation Theory, 95 (1998), 280-309.

  • Lyche, T. and K. Scherer, On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis, in Multivariate Approximation and Splines, G. Nürnberger, J. W. Schmidt, and G. Walz (eds.), ISNM.125, Birkhäuser Verlag, Basel, 1997, 141-151 . 

  • Lyche, T., and L. L. Schumaker, Total Positivity Properties of LB-splines, in Total Positivity and its Applications , M. Gasca
    and C. Micchelli (eds.), Kluwer, Dordrecht, 1996, 35--46. 

  • Lyche T., and K. Strøm, Knot insertion for Natural Splines, Annals of Numerical Mathematics 3 (1996), 221--246. 

  • Habib, A, R. Goldman, and T. Lyche, A Neville algorithm for multivariate Hermite interpolation, Journal of Computational and Applied Mathematics 73 (1996), 95--118. 

  • Koch, P. E., Lyche, T., M. Neamtu, and L. L. Schumaker, Control curves and knot insertion for trigonometric splines, Advances in Computational Mathematics, 4 (1995), 405--424. 

  • Dæhlen, M, and T. Lyche, Refinement techniques in computer graphics, Eurographics '94, annual conference, Star-Report 6.,3. 

  • Lyche, T., and L. L. Schumaker, L-spline wavelets, in Wavelets: Theory, Algorithms, and Applications, Charles K. Chui,
    Laura Montefusco, and Luigia Puccio (eds.), Academic Press, 1994, 197--212. 

  • Lyche, T., and K. Mørken, A metric for parametric approximation, in Curves and Surfaces in Geometric Design, P.-J. Laurent, A. Le Méhauté, and L. L. Schumaker, (eds.), A K Peters, Wellesley, 1994, 311--318. 

  • Dokken, T., and T. Lyche, Spline conversion, existing solutions, open problems, in Curves and Surfaces in Geometric Design, P.-J.
    Laurent, A. Le Méhauté, and L. L. Schumaker, (eds.), A K Peters, Wellesley, 1994, 121--130. 

  • Lyche, T., Knot removal for spline curves and surfaces, in Approximation Theory VII, E. W. Cheney, C. K. Chui, and L. L. Schumaker, (eds.), Academic Press, Boston, 1993, 207--227. 

  • Lyche, T., K. Mørken and K. Strøm, Conversion between B-spline bases,  in Knot Insertion and Deletion Algorithms for B-spline Curves and Surfaces, R. N. Goldman and T. Lyche (eds.), SIAM, Phil, 1993, 135--153. 

  • Lyche, T., and K. Mørken, How much can the size of the B-spline coefficients be reduced by inserting one knot?, in Knot Insertion and Deletion Algorithms for B-spline Curves and Surfaces, R. N. Goldman and T. Lyche (eds.), SIAM, Phil, 1993, 155--178. 

  • Lyche, T., and K. Mørken, Spline wavelets of minimal support, in Numerical Methods in Approximation Theory, Vol. 9, D. Braess and L. L. Schumaker (eds.), Birkhauser Verlag, Basel, 1992, 177--194. 

  • Koch, P. E., and T. Lyche, Interpolation with exponential B-splines in tension, Computing Supplements (1992), 173--190. 

  • Koch, P. E., and T. Lyche, Construction of exponential tension B-splines of arbitrary order, in Curves and Surfaces, P.-J. Laurent, A. Le Méhauté, and L. L. Schumaker (eds.), Academic Press, New York, 1991, 255--258. 

  • Dæhlen, M., and T. Lyche, Box splines and applications, in Geometric Modeling, H. Hagen and D. Roller (eds.), Springer-Verlag, Berlin,1991, 35--93. 

  • Dokken, T., M. Dæhlen , T. Lyche, and K. Mørken, Good approximation of circles by curvature-continuous Bézier curves, Computer Aided Geometric Design 7 (1990), 33--41. 

  • Lyche, T., Condition numbers for B-splines, in Numerical analysis 1989, D. F. Griffiths and G. A. Watson (eds.), Longman Scientific and Technical, Essex, 1990, 182--192.

  • Arge, E., M. Dæhlen, T. Lyche, and K. Mørken, Constrained spline approximation of functions and data based on constrained knot removal,  in Algorithms for Approximation II, J. C. Mason and M. G. Cox (eds.), Chapman and Hall, London, 1990, 4--20. 

  • Lyche, T., Discrete B-splines and conversion problems, in Computations of Curves and Surfaces, M. Gasca (ed.), Kluwer Academic Publishers, Dordrecht,1990, 117--134. 

  • Koch, P. E., and T. Lyche, Exponential B-splines in tension, in Approximation Theory VI", C. K. Chui, L. L. Schumaker, and J. D. Ward (eds.), Academic Press, New York, 1990, 361--364.





Published Jan. 28, 2013 1:38 PM - Last modified May 19, 2017 2:42 PM


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