Publications of Joab Winkler

    2005

  1. Winkler, J.R., Niranjan, M and Lawrence, N. D., (eds) Deterministic and Statistical Methods in Machine Learning, Lecture Notes in Computer Science 3635, Springer, Germany, 2005.
  2. Winkler, J.R., "A comparison of condition numbers for the full rank least squares problem", in Deterministic and Statistical Methods in Machine Learning, eds. J. Winkler, M. Niranjan and N. D. Lawrence, Lecture Notes in Computer Science 3635, Springer, Germany, 2005, 296-318.
  3. Winkler, J.R., "Backward errors and condition numbers of regular and singular points on algebraic curves", in Mathematics of Surfaces XI, eds. R. Martin, H. Bez and M. Sabin, Lecture Notes in Computer Science 3604, Springer, Germany, 2005, 413-433.
  4. Bini, D. A., Gemignani, L. and Winker, J.R., "Structured matrix methods for CAGD: An application to computing the resultant of polynomials in the Bernstein basis", Numerical Linear Algebra and Its Applications, 12, pp. 685-698, 2005.
  5. Winkler, J.R., "Numerical and algebraic properties of Bernstein basis resultant matrices", in Computational Methods for Algebraic Spline Surfaces, eds. Tor Dokken and Bert Juettler, Springer, Germany, 2005, 107-118.

    2004

  6. Winkler, J.R., "The transformation of the companion matrix resultant between the power and Bernstein polynomial bases", Applied Numerical Mathematics, 48, 1, pp. 113-126, 2004.

    2003

  7. Winkler, J.R., "A statistical analysis of the numerical condition of multiple roots of polynomials", Computers and Mathematics with Applications, 45, pp. 9-24, 2003.
  8. Winkler, J.R., "A companion matrix resultant for Bernstein polynomials", Linear Algebra and Its Applications, 362, pp. 153-175, 2003.
  9. Winkler, J.R. and Goldman, R.N., "The Sylvester resultant matrix for Bernstein polynomials", in Curve and Surface Design: Saint-Malo 2002, eds. Tom Lyche, Marie-Laurence Mazure and Larry L. Schumaker, Nashboro Press, Brentwood, Tennessee, USA, 2003, 407-416.

    2002

  10. Winkler, J.R. and Niranjan, M.N., (eds.) Uncertainty in Geometric Computations, Kluwer Academic Publishers, Massachusetts, USA, 2002.
  11. Winkler, J.R., "Properties of the companion matrix resultant for Bernstein polynomials", in Uncertainty in Geometric Computations, eds. J.R. Winkler and M. Niranjan, Kluwer Academic Publishers, Massachusetts, USA, 2002, 185-198.

    2001

  12. Winkler, J.R., "A tutorial on wavelets for inverse problems", invited paper at The British Workshop on Inverse Problems, Loughborough, UK, March 2001.
  13. Winkler, J.R., "Computational experiments with resultants for scaled Bernstein polynomials", in Mathematical Methods for Curves and Surfaces: Oslo 2000, eds. T. Lyche, L.L. Schumaker, Vanderbilt University Press, Nashville, Tennessee, USA, 2001, 535-544.
  14. Winkler, J.R., "Condition numbers of a nearly singular simple root of a polynomial", Applied Numerical Mathematics, 38, 3, pp. 275-285, 2001.
  15. Winkler, J.R., "A comparison of the average case numerical condition of the power and Bernstein polynomial bases", International Journal of Computer Mathematics, 77, pp. 583--602, 2001.
  16. Rees, J.M., Staszewski W.J. and Winkler, J.R., "Case study of a wave event in the stable atmospheric boundary layer overlying an Antarctic Ice Shelf using the orthogonal wavelet transform", Dynamics of Atmospheres and Oceans, 34, pp. 245-261, 2001.

    2000

  17. Winkler, J.R., "A resultant matrix for scaled Bernstein polynomials", Linear Algebra and Its Applications, 319, pp. 179-191, 2000.
  18. Winkler, J.R. and Ragozin, D.L., "A class of Bernstein polynomials that satisfy Descartes' rule of signs exactly", The Mathematics of Surfaces IX : Proceedings of the Ninth IMA Conference on The Mathematics of Surfaces, The University of Cambridge, 4-6 September 2000. Eds. Roberto Cipolla and Ralph Martin. Springer-Verlag, London, England. pp. 424-437, 2000.
  19. Winkler, J.R., "Wavelets via filter banks : theory and examples", ESGI 2000, 37th European Study Group with Industry, Sheffield, UK. April 2000.

    1999

  20. Winkler, J.R., "Backward error analysis of the roots of polynomials", Neural, Parallel and Scientific Computations, 7 (4), pp. 463-485, December 1999. See aslo 9 (1), pp. 91-96, March 2001.

    1998

  21. Winkler, J.R., "The applications of a companion matrix for Bernstein polynomials", Dept. of Computer Science Technical Report CS-98-03, University of Sheffield.
  22. Winkler, J.R., "The numerical condition of roots of polynomials in Bernstein form", The Mathematics of Surfaces VIII, Proceedings of the 8th IMA Conference on The Mathematics of Surfaces, ed. R. Cripps, University of Birmingham, England, 31 August-2 September 1998, 265-280.

    1997

  23. Winkler, J.R., "A companion matrix for Bernstein polynomials", 5th SIAM Conference on Geometric Design, Nashville, Tennessee, USA, November 3-6, 1997.
  24. Winkler, J.R., "Tikhonov regularisation in standard form for polynomial basis conversion", Applied Mathematical Modelling, 21, October 1997, 651-662.
  25. Winkler, J.R., "Polynomial basis conversion made stable by truncated singular value decomposition", Applied Mathematical Modelling, 21, September 1997, 557-568.
  26. Winkler, J.R., "An ill-conditioned problem in computer aided geometric design", Invited paper in Neural, Parallel and Scientific Computations, 5, 1&2, March & June 1997, 179-200.
  27. Winkler, J.R., "The condition number of a matrix and the stability of linear algebraic equations", Dept. of Computer Science Technical Report CS-97-05, University of Sheffield.
  28. Winkler, J.R., "A recurrence relationship for the transformation matrix between the power and Bernstein polynomial bases", Dept. of Computer Science Technical Report CS-97-06, University of Sheffield.
  29. Winkler, J.R., "Numerically stable conversion between the Bezier and B-spline forms of a curve", in Curves and Surfaces with Applications in CAGD, eds. A Le Mehaute, C. Rahut, L.L. Schumaker, Vanderbilt University Press, Nashville, Tennessee, USA, 1997, 465-472.

    1996

  30. Winkler, J.R., "Singular projective transformation matrices", Applied Mathematical Modelling, 20, October 1996, 771-778. Also, erratum to Singular projective transformation matrices, 20, November 1996.

    1995

  31. Winkler, J.R., "A comparison of two regularisation procedures for polynomial basis conversion", 4th SIAM Conference on Geometric Design, Nashville, Tennessee, USA, November 6-9, 1995.

    1994

  32. Winkler, J.R., "The sensitivity of linear algebraic equations", 5th SIAM Conference on Applied Linear Algebra, Snowbird, Utah, USA, June 15-18, 1994.

    1986

  33. Winkler, J.R., "Accurate field analysis of the propagation of elastic waves through an acoustic microscope. Part 1 : Theory", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, UFCC-33, no. 6, 644-656, 1986. With J. B. Davies.
  34. Winkler, J.R., "Accurate field analysis of the propagation of elastic waves through an acoustic microscope. Part 2 : Results", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, UFCC-33, no. 6, 657-668, 1986. With J.B. Davies.

    1984

  35. Winkler, J.R., "Elimination of spurious modes in finite element analysis", J. Comp. Phys. 56, 1, 1-14, 1984. With J.B. Davies.

Information on the computer-aided design research activities is in the computer-aided design web page

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