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Gershon Elber, Tom Grandine, "An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 4, pp. 596604, July/August, 2009.  
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@article{ 10.1109/TVCG.2009.42, author = {Gershon Elber and Tom Grandine}, title = {An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {15}, number = {4}, issn = {10772626}, year = {2009}, pages = {596604}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.42}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees IS  4 SN  10772626 SP596 EP604 EPD  596604 A1  Gershon Elber, A1  Tom Grandine, PY  2009 KW  Interval arithmetic KW  multivariate polynomial constraint solver KW  selfbisectors KW  contact computation KW  Hausdorff distance. VL  15 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] A.V. Aho, R. Sethi, and J.D. Ullman, Compilers: Principles, Techniques, and Tools. AddisonWesley, 1986.
[2] M. Bartoň and B. Jüttler, “Computing Roots of Polynomials by Quadratic Clipping,” Computer Aided Geometric Design, vol. 24, no. 3, pp. 125141, 2007.
[3] M. Bartoň, B. Jüttler, and B. Moore, “Polynomial Solvers with Superquadratic Convergence,” Proc. 10th SIAM Conf. Geometric Design & Computing, 2007.
[4] E. Cohen, R.F. Riesenfeld, and G. Elber, Geometric Modeling with Splines. A.K. Peters, 2001.
[5] G. Elber and T. Grandine, “Hausdorff and Minimal Distances between Parametric Freeforms in ${\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^2$ and ${\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^3$ ,” Proc. Int'l Conf. Advances in Geometric Modeling and Processing, pp. 191204, 2008.
[6] G. Elber, T. Grandine, and M.S. Kim, “Surface Self Intersection Computation via Algebraic Decomposition,” Computer Aided Design, to be published.
[7] G. Elber and M.S. Kim, “Geometric Constraint Solver Using Multivariate Rational Spline Functions,” Proc. Symp. Solid Modeling and Applications '01, pp. 110, 2001.
[8] L.H.D. Figueiredo and J. Stolfi, “Affine Arithmetic: Concepts and Applications,” Numerical Algorithms, vol. 37, pp. 147158, 2004.
[9] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness. W.H. Freeman and Company, 1979.
[10] I. Hanniel and G. Elber, “Subdivision Termination Criteria in Subdivision Multivariate Solvers,” Computer Aided Design, vol. 39, pp. 369378, 2007.
[11] J. Lane and R. Riesenfeld, “Bounds on a Polynomial,” BIT, vol. 21, pp. 112117, 1981.
[12] B. Mourrain and J.P. Pavone, “Subdivision Methods for Solving Polynomial Equations,” Technical Report RR5658, INRIA SophiaAntipolis, http://hal.inria.fr/inria00070350en/, 2006.
[13] T. Nishita, T.W. Sederberg, and M. Kakimoto, “Ray Tracing Trimmed Rational Surface Patches,” Proc. ACM SIGGRAPH '90, pp. 337345, 1990.
[14] M. Reuter, T.S. Mikkelsen, E.C. Sherbrooke, T. Maekawa, and N.M. Patrikalakis, “Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis,” The Visual Computer, vol. 24, no. 3, pp. 187200, 2008.
[15] E.C. Sherbrooke and N.M. Patrikalakis, “Computation of the Solutions of Nonlinear Polynomial Systems,” Computer Aided Geometric Design, vol. 10, no. 5, pp. 279405, 1993.
[16] C.K. Yap, “Robust Geometric Computation,” Handbook of Discrete and Computational Geometry, J.E. Goodman and J. O'Rourke, eds., second ed., chapter 41, pp. 927952, Chapman & Hall/CRC, 2004.