Name
Abstract | ||
|---|---|---|
Newton's method for finding a zero of a vectorial function is a powerful theoretical and practical tool. One of the drawbacks of the classical convergence proof is that closeness to a non-singular zero must be supposed a priori. Kantorovich's theorem on Newton's method has the advantage of proving existence of a solution and convergence to it under very mild conditions. This theorem holds in Banach spaces. Newton's method has been extended to the problem of finding a singularity of a vectorial field in Riemannian manifold. We extend Kantorovich's theorem on Newton's method to Riemannian manifolds. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jcom.2001.0582 | J. Complexity |
Keywords | DocType | Volume |
Riemannian manifold,mild condition,non-singular zero,Banach space,Riemannian Manifolds,practical tool,vectorial function,vectorial field,classical convergence proof | Journal | 18 |
Issue | ISSN | Citations |
1 | Journal of Complexity | 35 |
PageRank | References | Authors |
2.93 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| O. P. Ferreira | 1 | 78 | 6.41 |
| B. F. Svaiter | 2 | 608 | 72.74 |