Certified predictor–corrector tracking for Newton homotopies. (May 2016) - Hauenstein, Jonathan D.; Liddell, Alan C.
Abstract: We develop certified tracking procedures for Newton homotopies, which are homotopies for which only the constant terms are changed. For these homotopies, our certified procedures include using a constant predictor with Newton corrections, an Euler predictor with no corrections, and an Euler predictor with Newton corrections. In each case, the predictor is guaranteed to produce a point in the quadratic convergence basin of Newton's method. We analyze the complexity of a tracking procedure using a constant predictor with Newton corrections, with the number of steps bounded above by a constant multiple of the length of the path in the γ -metric. Examples are included to compare the behavior of these certified tracking methods.