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The SVD for Polynomial Systems

This is paper no. 8 in the list on p. gif. On my sabbatical I was invited to visit IBM T. J. Watson Research Center, a world-class institution for computer science research. During that time I wrote the paper ``The Singular Value Decomposition for Polynomial Systems'', with Barry Trager, Patrizia Gianni, and Stephen Watt. This work is perhaps the most significant and deepest scientific computing work I have done to date. The SNAP (Symbolic-Numeric Algorithms for Polynomials) conference, held July 15--17 1996 in Sophia-Antipolis, France, came into being to allow discussion of some of the consequences of the ideas raised in this paper. I continue to be active in this area (which is now beginning to be called Numerical Nonlinear Algebra); since SNAP I have published two SIGSAM bulletin technical articles on this, have had one further paper---joint with Gianni and Trager--- accepted for ISSAC '97 and have work in progress with Paulina Chin. The ISSAC '97 paper provides a starting point for the Ph.D. work of my new student, Raphael Okojie, who will be investigating the use of sparse eigenvalue technology for this problem.



Robert Corless
Fri Jan 9 10:52:31 EST 1998