Fast computation of zeros of polynomial systems with bounded degree under finite-precision
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 1279-1317 |
| Journal / Publication | Mathematics of Computation |
| Volume | 83 |
| Issue number | 287 |
| Online published | 10 Sept 2013 |
| Publication status | Published - May 2014 |
Link(s)
Abstract
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite precision. In this paper we describe a finite-precision version of this algorithm. Our main result shows that this version works within the same time bounds and requires a precision which, on the average, amounts to a polynomial amount of bits in the mantissa of the intervening floating-point numbers. © 2013 American Mathematical Society.
Research Area(s)
- Finite-precision, Polynomial systems, Smale's 17th problem
Citation Format(s)
Fast computation of zeros of polynomial systems with bounded degree under finite-precision. / Briquel, Irénée; Cucker, Felipe; Peña, Javier et al.
In: Mathematics of Computation, Vol. 83, No. 287, 05.2014, p. 1279-1317.
In: Mathematics of Computation, Vol. 83, No. 287, 05.2014, p. 1279-1317.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
