A generic position based method for real root isolation of zero-dimensional polynomial systems
2015
We improve the local generic position method for isolating the real roots of a zero-dimensional bivariate polynomial system with two polynomials and extend the method to general zero-dimensional polynomial systems. The method mainly involves resultant computation and real root isolation of univariate polynomial equations. The roots of the system have a linear univariate representation. The complexity of the method is O ? B ( N 10 ) for the bivariate case, where N = max ? ( d , ? ) , d resp., ? is an upper bound on the degree, resp., the maximal coefficient bitsize of the input polynomials. The algorithm is certified with probability 1 in the multivariate case. The implementation shows that the method is efficient, especially for bivariate polynomial systems.
Keywords:
- Reciprocal polynomial
- Combinatorics
- Matrix polynomial
- Discrete mathematics
- Minimal polynomial (field theory)
- Monic polynomial
- Mathematical optimization
- Resultant
- Wilkinson's polynomial
- Alternating polynomial
- Polynomial matrix
- Mathematics
- Symmetric polynomial
- Stable polynomial
- Polynomial
- Factorization of polynomials
- Correction
- Source
- Cite
- Save
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