Name
Abstract | ||
|---|---|---|
. We extend Smale’s concept of approximate zeros of an analytic function on a Banach space to two computational models that
account for errors in the computation: first, the weak model where the computations are done with a fixed precision; and second,
the strong model where the computations are done with varying precision. For both models, we develop a notion of robust approximate
zero and derive a corresponding robust point estimate.
A useful specialization of an analytic function on a Banach space is a system of integer polynomials. Given such a zero-dimensional
system, we bound the complexity of computing an absolute approximation to a root of the system using the strong model variant
of Newton’s method initiated from a robust approximate zero. The bound is expressed in terms of the condition number of the
system and is a generalization of a well-known bound of Brent to higher dimensions. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s11786-007-0005-7 | Mathematics in Computer Science |
Keywords | DocType | Volume |
point estimation,condition number,computer model,analytic function,banach space | Journal | 1 |
Issue | ISSN | Citations |
1 | 1661-8289 | 1 |
PageRank | References | Authors |
0.35 | 5 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vikram Sharma | 1 | 229 | 20.35 |