Matrix Methods for Solving Algebraic Systems

  • Ioannis Z. Emiris


The problem of computing all common zeros of a system of polynomials is of fundamental importance in a wide variety of scientific and engineering applications. This article surveys efficient methods based on the sparse resultant for computing all isolated solutions of an arbitrary system of n polynomials in n unknowns. In particular, we construct matrix formulae which yield nontrivial multiples of the resultant thus reducing root-finding to the eigendecomposition of a square matrix.


Matrix Polynomial Polynomial System Integer Point Mixed Volume Newton Polytopes 
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© Springer-Verlag Wien 2001

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  • Ioannis Z. Emiris

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