2004/08/30 by Anton Leykin, Leykin, Anton, Jan Verschelde +3
Computer Science · Engineering · #14Q99 #65H10 #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0408419
openalex publication_date 2004/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution as a regular root. Using standard bases, a tool for the symbolic computation of multiplicities, we show that the number of deflation stages is bounded by the multiplicity of the isolated root. Our implementation performs well on a large class of applications.