Numerical factorization of multivariate complex polynomials

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 reduc...

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Bibliographic Details
Published in:Theoretical computer science Vol. 315; no. 2; pp. 651 - 669
Main Authors: Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.
Format: Journal Article
Language:English
Published: Elsevier B.V 06.05.2004
Subjects:
Approximate factorization
Divided differences
Generic points
Homotopy continuation
Irreducible decomposition
Monodromy
Multiple roots
Newton interpolation
Numerical algebraic geometry
Polynomial
Stewart–Gough platform
Symbolic-numeric computation
Traces
Witness points
Polynomial
68W30
Secondary 65H10
Divided differences
14Q99
Multiple roots
Traces
Irreducible decomposition
Monodromy
Approximate factorization
Newton interpolation
Symbolic-numeric computation
Primary 13P05
Homotopy continuation
Witness points
Stewart–Gough platform
Generic points
Numerical algebraic geometry
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2004.01.011