Abstract
Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible decomposition. We define local witness sets and describe a numerical algebraic geometric approach for computing a numerical local irreducible decomposition for polynomial systems. Several examples are presented.
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CITATION STYLE
Brake, D. A., Hauenstein, J. D., & Sommese, A. J. (2016). Numerical local irreducible decomposition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9582, pp. 124–129). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_9
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