Finding the "truncated" polynomial that is closest to a function
| dc.creator | Brisebarre, Nicolas | |
| dc.creator | Muller, Jean-Michel | |
| dc.date | 2003-07-04 | |
| dc.date.accessioned | 2026-07-07T03:19:59Z | |
| dc.date.available | 2026-07-07T03:19:59Z | |
| dc.description | When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite - and sometimes small - number of bits: this is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-$i$ coefficient has at most $m_i$ fractional bits (in other words, it is a rational number with denominator $2^{m_i}$). We provide a general method for finding the best polynomial approximation under this constraint. Then, we suggest refinements than can be used to accelerate our method. | |
| dc.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/cs/0307009 | |
| dc.identifier | http://arxiv.org/abs/cs/0307009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/31682 | |
| dc.subject | Mathematical Software | |
| dc.subject | G.1.0, G.1.2, B.2.4 | |
| dc.title | Finding the "truncated" polynomial that is closest to a function | |
| dc.type | text |