An improved method for evaluating Max Noether conditions: case of breadth one

Authors:
Nan Li
Affiliations:
Key Laboratory of Mathematics Mechanization, AMSS, Beijing, China and INRIA, Paris-Rocquencourt, Le Chesnay, France
Venue:
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Year:
2012

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Abstract

For an isolated breadth-one singular solution xe of a polynomial system F = {f1,..., fn}, fi ∈ C[x1,..., xn] (breadth one means the Jacobian JF (xe) is of corank one), in [6, 7] we present a symbolic-numeric method to refine an approximate solution x with quadratic convergence if x is close to xe. A preliminary implementation performs well in case the approximate Max Noether conditions computed are sparse, but suffers from the evaluation of them when they are not. In this paper we describe how to avoid the linear transformation and evaluate Max Noether conditions efficiently by solving a sequence of least squares problems.