Tom Lyche

Image of Tom Lyche
Norwegian version of this page
Email tom@math.uio.no
Mobile phone +47-48357266
Room 1229
Username
Visiting address Niels Henrik Abels hus Moltke Moes vei 35 0851 Oslo
Postal address Postboks 1053 Blindern 0316 Oslo

Academic Interests

  • Approximation Theory 
  • Numerical Analysis
  • Spline Theory
  • Isogeometric Analysis
 books:

  1. Lyche, T. and J-L Merrien, Exercises in Computational Mathematics with MATLAB, Problem Books in Mathematics, https://doi.org/10.1007/978-3-662-43511-3 Springer Verlag, Heidelberg, 2014, 372 pages.

  2. Lyche, T., Numerical Linear Algebra and Matrix Factorizations, Texts in Computational Science and Engi- neering 22, https://doi.org/10.1007/978-3-030-36468-7, Springer Nature Switzerland AG, 2020, 371 pages.

  3. Lyche, T, Muntingh, G and Ø. Ryan, Exercises in Numerical Linear Algebra and Matrix Factorizations, Texts in Computational Science and Engineering 23, ISBN 978-3-030-59788-7, Springer Nature Switzerland AG, 2020, 365 pages.

Higher education and employment history

Education

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.

Honoraria

  • 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.

Appointments

  • 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.

Cooperation

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

March 2023                 Visiting professor INSA, Univ. Rennes, France

January 15-25 2023     Visit Universita di Roma “Tor Vergata”

Sept 2018                    Lecturer RMschool 2018, Universita di Roma “Tor Vergata”

Oct-Jan, 2015/16        Visiting professor, Universita di Roma “Tor Vergata”

2005-2022                   Regular visits to Universita di Roma “Tor Vergata”

2003-2022                   Regular visits to Univ. of Rennes, France

1984-2020                   Regular visits to Univ. of Utah, USA

               April 0,2, 2005              Univ. di Siena

April-May 2000            Univ. of Grenoble, France

June-Aug. 1983           Univ. of Utah, USA

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

    

Selected publications

 

  • Lyche,T. Mørken, K., and Reif, U., On the condition of cubic B-splines, J. Approx. Th. (289) publisehd online 2023, https://doi.org/10.1016/j.jat.2023.105883

  • Lyche, T., Manni, C. and Speleers, H., Construction of C2 cubic splines on arbitrary triangulations. Foundations of Computational Mathematics 22(5), 1309–1350, 2022, https://doi.org/10.1007/s10208-022-09553-z.

  • Lyche, T., Merrien, JL, and Sauer, T., Simplex-Splines on the Clough- Tocher Split with Arbitrary Smoothness. In: Geometric Challenges in Iso geometric Analysis, Manni, C., Speleers, H. (eds) , Springer INdAM Series, vol 49. Springer, Cham. pp 85–121,2022. ISBN 978-3-030-92312-9. https://doi.org/10.1007/978-3-030-92313-6.

  • Bressan, A., Lyche, T. Local Approximation from Spline Spaces on Box Meshes, Found. Comput. Math. 21(2021), 807–848. Published online 07 July, 2020. https://doi.org/10.1007/s10208-020-09467-8

  • Lyche, T. and G. Muntingh, B-spline-like bases for C2 cubics on the Powell–Sabin 12-split, SMAI Journal of Computational Mathematics, S5(2019), 129–159.

  • Lyche, T., Manni, C. and Speleers, H., Tchebycheffian B-Splines Revisited: An Introductory Exposition, in Advanced Methods for Geometric Modeling and Numerical Simulation, Carlotta Gianelli and Hendrik Speleers (eds.), Springer INdAM Series, (2019), 179–216.

  • Bracco, C., Lyche, T., Manni, C. and Speleers, H., Tchebycheffian spline spaces over planar T-meshes: Dimension bounds and dimension instabilities, J. Comp. and Applied Math. , 349(2019), 265-278.

  • Lyche, T., Manni, C. and Speleers, H., Foundations of Spline Theory: B- Splines, Spline Approximation and Hierarchical Refinement, in Splines and PDEs: From Approximation Theory to Numerical Linear Algebra, Cetraro, Italy 2017, LNMCIME volume 2219, Lyche, T., C. Manni and H. Speleers (Eds.), 2018 Springer Nature Switzerland AG, 2018, 1–76.

  • Lyche, T. and Merrien, J-L, Simplex-splines on the Clough–Tocher element, Computer-Aided Geom. Design 65(2018), 76–92

  • Lyche, T. and G. Muntingh, Stable Simplex Spline Bases for C3 Quintics on the Powell–Sabin 12-Split, Constr. Approx. 45(2017), 1–32.

  • 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. http://dx.doi.org/10.1016/j.cagd.2016.01.002.
  • Cesare Bracco , Tom Lyche, Carla Manni, Fabio Roman, Hendrik Speleers, Generalized 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.

  • 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 Fa`a di Bruno’s formula, Math. Comp. , 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’, Constr. Approx. , 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 8 (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 Mar. 21, 2023 12:06 PM - Last modified Mar. 21, 2023 12:06 PM

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