Higher-order Deflation for Polynomial Systems with Isolated Singular Solutions

@inproceedings{Leykin2007HigherorderDF,
  title={Higher-order Deflation for Polynomial Systems with Isolated Singular Solutions},
  author={Anton Leykin and Jan Verschelde and Ailing Zhao},
  year={2007}
}
Given an approximation to a multiple isolated solution of a system of polynomial equations, we provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton’s method. Using first-order derivatives of the polynomials in the system, our first-order deflation method creates an augmented system that has the multiple isolated solution of the original system as a regular solution. In this paper we consider two approaches to computing the “multiplicity structure” at a… CONTINUE READING