Paper Info
Title
Numerical factorization of multivariate complex polynomials
Abstract
One can consider the problem of factoring multivariate complex polynomials as a special case of the decomposition of a pure dimensional solution set of a polynomial system into irreducible components. The importance and nature of this problem however justify a special treatment. We exploit the reduction to the univariate root finding problem as a way to sample the polynomial more efficiently, certify the decomposition with linear traces, and apply interpolation techniques to construct the irreducible factors. With a random combination of differentials we lower multiplicities and reduce to the regular case. Estimates on the location of the zeroes of the derivative of polynomials provide bounds on the required precision. We apply our software to study the singularities of Stewart-Gough platforms.
Year
DOI
Venue
2004
10.1016/j.tcs.2004.01.011
Theor. Comput. Sci.
Keywords
DocType
Volume
irreducible component,Stewart-Gough platform,Divided differences,special case,multivariate complex polynomial,multiple roots,numerical algebraic geometry,special treatment,traces,Symbolic-numeric computation,68W30,Numerical algebraic geometry,monodromy,approximate factorization,Homotopy continuation,Traces,polynomial system,witness points.,Generic points,Multiple roots,generic points,Approximate factorization,interpolation technique,symbolic-numeric computation,Stewart–Gough platform,stewart-gough platform,Polynomial,Newton interpolation,Witness points,Monodromy,irreducible decomposition,irreducible factor,divided difierences,homotopy continuation,Primary 13P05,linear trace,14Q99,Secondary 65H10,Irreducible decomposition,numerical factorization,newton interpolation,regular case,polynomial
Journal
315
Issue
ISSN
Citations 
2-3
Theoretical Computer Science
19
PageRank 
References 
Authors
1.19
20
3
Name
Order
Citations
PageRank
Andrew J. Sommese141239.68
Jan Verschelde267664.84
Charles W. Wampler341044.13