Name
Abstract | ||
|---|---|---|
This article treats numerical methods for tracking an implicitly defined path. The numerical precision required to successfully track such a path is difficult to predict a priori, and indeed it may change dramatically through the course of the path. In current practice, one must either choose a conservatively large numerical precision at the outset or rerun paths multiple times in successively higher precision until success is achieved. To avoid unnecessary computational cost, it would be preferable to adaptively adjust the precision as the tracking proceeds in response to the local conditioning of the path. We present an algorithm that can be set to either reactively adjust precision in response to step failure or proactively set the precision using error estimates. We then test the relative merits of reactive and proactive adaptation on several examples arising as homotopies for solving systems of polynomial equations. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/060658862 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
tracking proceed,numerical precision,numerical method,current practice,large numerical precision,higher precision,error estimate,adaptive multiprecision path tracking,local conditioning,multiple time,rerun path | Mathematical optimization,Condition number,Polynomial,Control theory,A priori and a posteriori,System of polynomial equations,Homotopy,Numerical analysis,Numerical linear algebra,Mathematics,Calculus,Path tracking | Journal |
Volume | Issue | ISSN |
46 | 2 | 0036-1429 |
Citations | PageRank | References |
35 | 2.59 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel J. Bates | 1 | 103 | 12.03 |
| Jonathan D. Hauenstein | 2 | 269 | 37.65 |
| Andrew J. Sommese | 3 | 412 | 39.68 |
| Charles W. Wampler, II | 4 | 134 | 24.01 |