HJLS algorithm ( Integer Relation): Difference between revisions
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(Created page with "== Time Complexity == $O(n^{3}(n+k)$) == Space Complexity == $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable (Derived: Store Gram-Schmidt basis vectors b_i (n n-dimensional vectors) and Gram-Schmidt numbers \mu_{i,j} (i and j both from 1 to n), not sure how to take into account the "bit complexity" part) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == bit...") |
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== Time Complexity == | == Time Complexity == | ||
$O(n^{3}(n+k)$ | $O(n^{3}(n+k))$ | ||
== Space Complexity == | == Space Complexity == | ||
$O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable | $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable bits | ||
(Derived: Store Gram-Schmidt basis vectors b_i (n n-dimensional vectors) and Gram-Schmidt numbers \mu_{i,j} (i and j both from 1 to n), not sure how to take into account the "bit complexity" part) | (Derived: Store Gram-Schmidt basis vectors b_i (n n-dimensional vectors) and Gram-Schmidt numbers \mu_{i,j} (i and j both from 1 to n), not sure how to take into account the "bit complexity" part) | ||
Latest revision as of 09:24, 28 April 2023
Time Complexity
$O(n^{3}(n+k))$
Space Complexity
$O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable bits
(Derived: Store Gram-Schmidt basis vectors b_i (n n-dimensional vectors) and Gram-Schmidt numbers \mu_{i,j} (i and j both from 1 to n), not sure how to take into account the "bit complexity" part)
Description
Approximate?
Exact
Randomized?
No, deterministic
Model of Computation
bit complexity
Year
1986
Reference
https://epubs-siam-org.ezproxy.canberra.edu.au/doi/pdf/10.1137/0218059