Tom Lyche

Professor of Computer Science
University of Oslo
phone:(47)22856024, fax (47)22852401

Tom Lyche has been on the faculty of the University of Oslo since 1972. He has been associated with the Department of Informatics since its creation in 1977, and was its first Chairman. He belongs to the Computational Mathematics research group. He is a member of CMA Centre of Mathematics for Applications. He is a member of the Norwegian Academy of

Science and Letters and is currently the leader of the Mathematical Sciences group in the Academy.

 

 

Research Interests
  • Geometric Modelling
  • Computer Graphics
  • Numerical Analysis
  • Approximation Theory

Teaching Interests

 


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Complete List of Papers

Recent publications

http://heim.ifi.uio.no/graphics/greenball.gif Lyche, T., K. Mørken, and F. Pelosi, Stable, linear spline wavelets on nonuniform knots with vanishing moments, Computer Aided Geometric Design, .

http://heim.ifi.uio.no/graphics/greenball.gif Lyche, T., C. Manni, and P. Sablonniere, Quasi-interpolation projectors for Box Splines, J. Comp. and Appled Math.,

http://heim.ifi.uio.no/graphics/greenball.gifFloater, M and T. Lyche, Divided differences of inverse functions and

partitions of a convex polygon, Math. Comp, 77(2008), 2295 – 2308.

 

http://heim.ifi.uio.no/graphics/greenball.gifFloater, M and T. Lyche, Two Chain Rules for Divided Differences and Faà di Bruno’s Formula, Math. Comp, 76(2007), 867 – 877.

 

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and J-L Merrien, Hermite subdivision with shape constraints on a rectangular mesh, BIT, 46(2006), 831 - 859.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and K. Scherer, Mixed norm condition numbers for the univariate Bernstein basis, Banach Center Publications, 72( 2006), 177 – 188..

 

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and K. Scherer, Addendum to ”On the L1-Condition Number of the Univariate Bernstein Basis”, Constructive Approximation, 24 (2006), 239 – 243.

 

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and J-L Merien, C1 Interpolatory Subdivision with Shape Constraints for Curves, Siam J. Numer. Anal.,  44 (2006), 1095 – 1121.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T and M-L Mazure, On the Existence of Piecewise Exponential B-splines, Advances in Computational Mathematics, 25 (2006), 105  - 133..

http://heim.ifi.uio.no/graphics/greenball.gifCostantini, P., Lyche,T., and Manni,C., On a Class of Weak Tchebycheff Systems, Numer. Math., 101(2005),333-354.

http://heim.ifi.uio.no/graphics/greenball.gifSederberg, 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.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T and J. M. Peña, Optimally Stable Multivariate Bases, Advances in Computational Mathematics, 20 (2004), 149 - 159.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and K. Scherer, On the L1-condition number of the univariate Bernstein basis, Constructive Approximation, 18 (2002),503 - 528.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. K. Nilssen,and R. Winther, Preconditioned Iterative Methods for Scattered Data Interpolation, Advances in Computational Mathematics, 17 (2002), 237 - 256.

http://heim.ifi.uio.no/graphics/greenball.gifByung-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.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, 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.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, 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.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and K. Scherer, On the p-norm Condition Number of the Multivariate Triangular Bernstein Basis, J. Comput. Appl. Math., 119 (2000), 259-273.

http://heim.ifi.uio.no/graphics/greenball.gifDæhlen, M., T. Lyche, K. Mørken, R. Schneider, and H-P. Seidel, Multiresolution analysis based on quadratic Hermite interpolation on triangles, J. Comput. Appl. Math., 119 (2000), 97--114.

http://heim.ifi.uio.no/graphics/greenball.gifFloater, M. and Lyche, T., Asymptotic Convergence of Degree-Raising, Advances in Comp. Math. 12 (2000), 175-187.

http://heim.ifi.uio.no/graphics/greenball.gifStark, 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

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T. and K. Mørken, The sensitivity of spline functions to perturbations of the knots, BIT 39 (1999), 305-322.

http://heim.ifi.uio.no/graphics/greenball.gifDyn, 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 Schumaker (eds.) Vanderbilt University Press, Nashville,33-38, 1998.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, T., L. L. Schumaker, and S. Stanley, Quasi-interpolants Based on Trigonometric Splines, J. Approx. Theory, 95 (1998), 280-309.

http://heim.ifi.uio.no/graphics/greenball.gifLyche, 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 .

Conferences and meetings:

http://heim.ifi.uio.no/graphics/greenball.gifPerspectives in Numerical Analysis, Helsinki University of Technology, May 27-29, 2008

http://heim.ifi.uio.no/graphics/greenball.gif Seventh International Conference on   Mathematical Methods for Curves and Surfaces  Toensberg, Norway, June 26 – July 1, 2008

http://heim.ifi.uio.no/graphics/greenball.gif 7th INTERNATIONAL CONFERENCE ON MULTIVARIATE APPROXIMATION, Haus Bommerholz, September 21  – 26, 2008

Member Editorial Boards

http://heim.ifi.uio.no/graphics/greenball.gifAdvances in Computational Mathematics

http://heim.ifi.uio.no/graphics/greenball.gifBIT

http://heim.ifi.uio.no/graphics/greenball.gifComputer Aided Geometric Design

 

http://heim.ifi.uio.no/graphics/greenball.gifJournal of Computational and Applied Mathematics

Books edited

·         Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. L. Schumaker (eds.), Academic Press, New York, 1989

·         Mathematical Methods in Computer Aided Geometric Design II, T. Lyche and L. L. Schumaker (eds.), Academic Press, New York, 1992

·         Knot Insertion and Deletion Algorithms for B-spline Curves and Surfaces, Goldman, R. N. and T. Lyche (eds.), SIAM, Phil, 1993.

·         Trends in Approximation Theory, K. Kopotun,T. Lyche and M. Neamtu (eds.), Vanderbilt University Press, Nashville, 2001

http://heim.ifi.uio.no/graphics/greenball.gifMathematical Methods for Curves and Surfaces, M. Daehlen, T. Lyche, and L. L. Schumaker, (eds.), Vanderbilt University Press, 1995.

http://heim.ifi.uio.no/graphics/greenball.gifMathematical Methods for Curves and Surfaces II, M. Daehlen, T. Lyche, and L. L. Schumaker, (eds.), Vanderbilt University Press, 1998.

http://heim.ifi.uio.no/graphics/greenball.gifMathematical Methods in CAGD: Oslo 2000, T. Lyche, and L. L. Schumaker, (eds.), Vanderbilt University Press, 2001.

http://heim.ifi.uio.no/graphics/greenball.gifCurve and Surface Design: Saint Malo 2002, , T. Lyche, M-L Mazure, and L. L. Schumaker (eds.), Nashboro Press, 2003.

http://heim.ifi.uio.no/graphics/greenball.gifFrom Object-Orientation to Formal Methods, Essays in Memory of Ole-Johan Dahl, LNCS 2635, Springer, Berlin, 2004.

            http://heim.ifi.uio.no/graphics/greenball.gif Curve and Surface Design: Avignon 2006, P. Chenin, Lyche, T., and L.   L. Schumaker (eds.), Nashboro Press, Nashville, TN,

2007, 285 pages.

Postal address

CMA and Department of Informatics
P. O. Box 1053, Blindern
0316 Oslo
Norway

Visiting address

The Niels Henrik Abel Building, room B1015
Moltke Moe's vei 35
N-0349 Oslo