Pseudozeros of multivariate polynomials
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- by J. William Hoffman, James J. Madden and Hong Zhang PDF
- Math. Comp. 72 (2003), 975-1002 Request permission
Abstract:
The pseudozero set of a system $f$ of polynomials in $n$ complex variables is the subset of $\mathbf {C}^n$ which is the union of the zero-sets of all polynomial systems $g$ that are near to $f$ in a suitable sense. This concept is made precise, and general properties of pseudozero sets are established. In particular it is shown that in many cases of natural interest, the pseudozero set is a semialgebraic set. Also, estimates are given for the size of the projections of pseudozero sets in coordinate directions. Several examples are presented illustrating some of the general theory developed here. Finally, algorithmic ideas are proposed for solving multivariate polynomials.References
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Additional Information
- J. William Hoffman
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: hoffman@math.lsu.edu
- James J. Madden
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: madden@math.lsu.edu
- Hong Zhang
- Affiliation: Department of Computer Science, Illinois Institute of Technology, Chicago, Illinois 60616
- Email: hzhang@mcs.anl.gov
- Received by editor(s): May 5, 2000
- Received by editor(s) in revised form: April 24, 2001
- Published electronically: May 15, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 975-1002
- MSC (2000): Primary 65H10; Secondary 13P99, 14Q99, 14P10
- DOI: https://doi.org/10.1090/S0025-5718-02-01429-1
- MathSciNet review: 1954980