document: Quadratic Newton iteration for systems with multiplicity Newton 's iterator is one of the most popular components of polynomial equation system solvers , either from the numeric or symbolic point of view . This iterator usually handles smooth situations only -LRB- when the Jacobian matrix associated to the system is invertible -RRB- . This is often a restrictive factor . Generalizing Newton 's iterator is still an open problem : How to design an efficient iterator with a quadratic convergence even in degenerate cases ? We propose an answer for an m-adic topology when the ideal m can be chosen generic enough : compared to a smooth case we prove quadratic convergence with a small overhead that grows with the square of the multiplicity of the root
doc_bio_tags: B I I O B I I O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O
extractive_keyphrases: quadratic newton iteration systems with multiplicity polynomial equation system solvers jacobian matrix quadratic convergence
abstractive_keyphrases: newton's iterator m-adic topology