Newton's method is widely used to solve nonlinear problems because of its local quadratic convergence. Its convergence slows down and may even get lost when approaching solutions where the rank of the Jacobian matrix drops. We can restore the quadratic convergence by a modified deflation procedure, developed jointly with Anton Leykin and Ailing Zhao. Computational experiments on a large class of polynomial systems show that our deflation is a reconditioning method.
CAM colloquium , University of Notre Dame, 10 April 2006.