Graduate Students

• Danko Adrovic
  • Danko Adrovic and Jan Verschelde: Tropical Algebraic Geometry in Maple, a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients. The abstract and manuscript. Journal of Symbolic Computation 46(7):755-772, 2011.
  • Danko Adrovic and Jan Verschelde: Polyhedral Methods for Space Curves Exploiting Symmetry. The abstract and manuscript.
  • Danko Adrovic and Jan Verschelde: Computing Puiseux Series for Algebraic Surfaces. The abstract and manuscript.
• Genady Yoffe
  • Jan Verschelde and Genady Yoffe: Polynomial Homotopies on Multicore Workstations. The abstract and manuscript. In PASCO 2010, Proceedings of the 2010 International Workshop on Parallel Symbolic Computation, edited by Marc Moreno Maza and Jean-Louis Roch, pages 131-140, ACM 2010.
  • Jan Verschelde and Genady Yoffe: Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking. The abstract and manuscript.
  • Jan Verschelde and Genady Yoffe: Evaluating polynomials in several variables and their derivatives on a GPU computing processor. The abstract and manuscript.

Alumni

• Yusong Wang: Computing Dynamic Output Feedback Laws with Pieri Homotopies on a Parallel Computer. PhD thesis, UIC, Spring 2005. (first job: postdoc at Argonne National Laboratory)
  • Jan Verschelde and Yusong Wang: Computing Dynamic Output Feedback Laws. The Abstract and gzipped postscript file, of the revised manuscript in pdf format. Data consists of input and output. IEEE Transactions on Automatic Control 49(8):1393-1397, 2004.
  • Jan Verschelde and Yusong Wang: Computing Feedback Laws for Linear Systems with a Parallel Pieri Homotopy. The Abstract and manuscript in pdf format. Proceedings of the 2004 International Conference on Parallel Processing Workshops. 15-18 August 2004. Montreal, Quebec, Canada. High Performance Scientific and Engineering Computing. Edited by Yuanyuan Yang. Pages 222-229, IEEE Computer Society, 2004.
  • Jan Verschelde and Yusong Wang: Numerical Homotopy Algorithms for Satellite Trajectory Control by Pole Placement. The Abstract and Revised gzipped postscript file, manuscript in pdf format. Proceedings of MTNS 2002, Mathematical Theory of Networks and Systems (CDROM), Notre Dame, August 12-16, 2002.
• Ailing Zhao: Newton's Method with Deflation for Isolated Singularities of Polynomial Systems. PhD thesis, UIC, Summer 2007. (first job at Wolfram Research)
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions. The Abstract, manuscript in gzipped ps, and in pdf format.
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Evaluation of Jacobian Matrices for Newton's Method with Deflation to approximate Isolated Singular Solutions of Polynomial Systems. The Abstract, manuscript in gzipped ps, and in pdf format. In SNC 2005 Proceedings. International Workshop on Symbolic-Numeric Computation. Xi'an, China, July 19-21, 2005. Edited by Dongming Wang and Lihong Zhi. Pages 19-28, 2005. Revised manuscript in gzipped ps and pdf format.
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Newton's method with deflation for isolated singularities of polynomial systems. The Abstract, revised manuscript in gzipped ps, and in pdf format. Theoretical Computer Science 359(1-3): 111-122, 2006.
• Mina Khan: Certifying Approximate Solutions of Polynomial Systems, MS Thesis, UIC, Summer 2007.
• Yan Zhuang: Parallel Implementation of Polyhedral Homotopy Methods. PhD thesis, UIC, Summer 2007. (first job at Wolfram Research)
  • Jan Verschelde and Yan Zhuang: Parallel Implementation of the Polyhedral Homotopy Method. The Abstract, revised manuscript in gzipped ps, and in pdf format. Proceedings of the 2006 International Conference on Parallel Processing Workshops. 14-18 Augustus 2006. Columbus, Ohio. High Performance Scientific and Engineering Computing. Edited by Timothy Mark Pinkston and Fusun Ozguner. Pages 481-488, IEEE Computer Society, 2006.
  • Anton Leykin, Jan Verschelde, and Yan Zhuang: Parallel Homotopy Algorithms to Solve Polynomial Systems. The Abstract, manuscript in gzipped ps, and in pdf format. Proceedings of ICMS 2006, LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama. Pages 225-234, Springer-Verlag, 2006.
• Kathy Piret: Computing Critical Points of Polynomial Systems using PHCpack and Python. PhD Thesis, UIC, Summer 2008. (first job at Harold Washington College)
  • Kathy Piret and Jan Verschelde: Sweeping Algebraic Curves for Singular Solutions. The abstract and revised manuscript, Journal of Computational and Applied Mathematics 234(4): 1228-1237, 2010.
• Yun Guan: Numerical Homotopies for Algebraic Sets on a Parallel Computer. PhD Thesis, UIC, Summer 2010. (first job: visiting lecturer at UIC)
  • Yun Guan and Jan Verschelde: PHClab: A MATLAB/Octave interface to PHCpack. The abstract, the poster, and paper . In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer-Verlag, 2008.
  • Yun Guan and Jan Verschelde: Parallel Implementation of a Subsystem-by-Subsystem Solver. The abstract and manuscript. In the proceedings of the 22th High Performance Computing Symposium, Quebec City, 9-11 June 2008. Pages 117-123. IEEE Computer Society, 2008.
  • Yun Guan and Jan Verschelde: Sampling Algebraic Sets in Local Intrinsic Coordinates. The abstract and manuscript. Computers and Mathematics with Applications 62(10): 3706-2721, 2011.