Evaluation of Jacobian Matrices for Newton ’ s Method with Deflation to approximate Isolated Singular Solutions of Polynomial Systems

@inproceedings{Leykin2005EvaluationOJ,
title={Evaluation of Jacobian Matrices for Newton ’ s Method with Deflation to approximate Isolated Singular Solutions of Polynomial Systems},
author={Anton Leykin and Jan Verschelde and Ailing Zhao},
year={2005}
}

For isolated singular solutions of polynomial systems, we can restore the quadratic convergence of Newton’s method by deflation. The number of deflation stages is bounded by the multiplicity of the root. A preliminary implementation performs well in case only a few deflation stages are needed, but suffers from expression swell as the number of deflation stages grows. In this paper we describe how a directed acyclic graph of derivative operators guides an efficient evaluation of the Jacobian… CONTINUE READING