Name
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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.jsc.2015.07.001 | Journal of Symbolic Computation |
Keywords | Field | DocType |
Certified tracking,Alpha theory,Numerical algebraic geometry,Homotopy continuation,Newton's method | Applied mathematics,Discrete mathematics,Bounded set,Numerical algebraic geometry,Euler's formula,Rate of convergence,Homotopy continuation,Predictor–corrector method,Multiple,Calculus,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
74 | C | 0747-7171 |
Citations | PageRank | References |
3 | 0.40 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan D. Hauenstein | 1 | 269 | 37.65 |
| Alan C. Liddell Jr. | 2 | 18 | 2.88 |