Integer Relation Among Reals (Integer Relation)
Revision as of 10:25, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Integer Relation Among Reals (Integer Relation)}} == Description == Given a vector $x \in \mathbb{R}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$ == Related Problems == Subproblem: Integer Relation Among Integers == Parameters == <pre>n: dimensionality of vectors</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !!...")
Description
Given a vector $x \in \mathbb{R}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$
Related Problems
Subproblem: Integer Relation Among Integers
Parameters
n: dimensionality of vectors
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| HJLS algorithm | 1986 | $O(n^{3}(n+k)$) | $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable | Exact | Deterministic | Time |