Skip to main content
SpringerLink
Log in

Parallel Dixon Matrices by Bracket

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

It is known that the Dixon matrix can be constructed in parallel either by entry or by diagonal. This paper presents another parallel matrix construction, this time by bracket. The parallel by bracket algorithm is the fastest among the three, but not surprisingly it requires the highest number of processors. The method also shows analytically that the Dixon matrix has a total of m(m+1)2(m+2)n(n+1)2(n+2)/36 brackets but only mn(m+1)(n+1)(mn+2m+2n+1)/6 of them are distinct.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Boehm and P. Hartmut, Geometric Concepts for Geometric Design (Wellesley, Massachusetts, 1994).

    Google Scholar 

  2. E.W. Chionh, Concise parallel Dixon determinant, Comput. Aided Geom. Design 14 (1997) 561–570.

    Google Scholar 

  3. E.W. Chionh and R.N. Goldman, Elimination and resultants, IEEE Comput. Graphics Appl. 15(1) (1995) 69–77, 15(2) (1995) 60–69.

    Google Scholar 

  4. E.W. Chionh, M. Zhang and R.N. Goldman, Fast computation of the Bezout and the Dixon resultant matrices, J. Symbolic Comput. 33(1) (2002) 13–29.

    Google Scholar 

  5. D. Cox, J. Little and D.O'Shea, Using Algebraic Geometry (Springer, New York, 1998).

    Google Scholar 

  6. A.L. Dixon, The eliminant of three quantics in two independent variables, Proc. London Math. Soc. 6 (1908) 49–69, 473–492.

    Google Scholar 

  7. I.Z. Emiris and B. Mourrain, Matrices in elimination theory, J. Symbolic Comput. 28(1/2) (1999) 3–44.

    Google Scholar 

  8. F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. (1902) 3–27.

  9. D.Manocha and J.F. Canny, Algorithms for implicitizing rational parametric surfaces, Comput. Aided Geom. Design 9(1) (1992) 25–50.

    Google Scholar 

  10. W. Schreiner, C. Mittermaier and F. Winkler, Plotting algebraic space curves by cluster computing, in: Proc. of the 4th Asian Symposium on Computer Mathematics (World Scientific, Singapore, 2000).

    Google Scholar 

  11. T.W. Sederberg, D.C. Anderson and R.N. Goldman, Implicit representations of parametric curves and surfaces, Comput. Vision Graphics Image Process. 28 (1984) 72–84.

    Google Scholar 

  12. D. Wang, Elimination Methods (Springer, Wien, 2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing, National University of Singapore, Singapore, 117543

    Eng-Wee Chionh

Authors
  1. Eng-Wee Chionh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chionh, EW. Parallel Dixon Matrices by Bracket. Advances in Computational Mathematics 19, 373–383 (2003). https://doi.org/10.1023/A:1024264830187

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024264830187

Search

Navigation