MCS 595 Graduate Seminar, Spring 2005

This semester, we plan to meet again weekly in 712 SEO on Thursdays at 3PM.
  1. Thu 20 Jan: "Evaluation of Deflation Matrices". Repeated deflation with Newton's method restores the quadratic convergence when sufficiently close to an isolated singularity. The deflation involves the addition of a random combination of R+1 columns of the Jacobian matrix, where R is the numerical rank. When executed symbolically, the occurrence of expression swell allows only a couple of deflations. We show that we can "unwind" the multipliers using a derivative tree structure.
  2. Thu 3 Feb: "Solving Polynomial Systems using Homotopies I". A preview to the first one hour tutorial at ISSAC 2005.
  3. Thu 17 Feb: Anton Leykin on "Modelling monodromy decomposition method".
  4. Thu 24 Feb: Yusong Wang on "Computing dynamic output feedback laws with Pieri homotopies on a parallel computer".
  5. Thu 3 Mar: "Factoring Pure Dimensional Solution Sets of Polynomial Systems in Parallel".
  6. Thu 10 Mar: "Solving Polynomial Systems", a preview to the graduate student colloquium of Friday 11 March.
  7. Tue 15 Mar: "Homotopies for Numerical Irreducible Decomposition", in the Computational Commutative Algebra seminar.
  8. Thu 31 Mar: "Solving polynomial systems equation by equation".
  9. Thu 7 Apr: Ailing Zhao on "Numerical Rank-Revealing Method".
  10. Tue 12 Apr: "Secondary Polytopes", in the Computational Commutative Algebra seminar.
  11. Mon 2 May: Anton Leykin on "Computing the multiplicity structure at the isolated singular solution of a polynomial systems of equations. Algorithms of Dayton-Zeng and Stetter-Thallinger.
We may meet less frequently this semester, but note the Computational Commutative Algebra seminar organized by Anton Leykin.

Seminars organized in previous semesters: