Determinant of Matrices with Integer Entries: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Determinant of Matrices with Integer Entries - Time.png|1000px]] | [[File:Determinant of Matrices with Integer Entries - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Determinant of Matrices with Integer Entries - Space.png|1000px]] | [[File:Determinant of Matrices with Integer Entries - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Determinant of Matrices with Integer Entries - Pareto Frontier.png|1000px]] | [[File:Determinant of Matrices with Integer Entries - Pareto Frontier.png|1000px]] | ||
Revision as of 13:05, 15 February 2023
Description
Calculate the determinant of a given matrix with integer matrices. For such matrices, the determinant is also an integer.
Parameters
n: dimension of matrix
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Bareiss algorithm | 1968 | $O(n^{5}L^{2} (log(n)$^{2} + L^{2})) | $O(n^{2}(n*log(n)$+nL)) | Exact | Deterministic | Time |
| Bareiss algorithm with fast multiplication | 1968 | $O(n^{4}L(log(n)$ + L)log(log(n) + L)) | $O(n^{2}(n*log(n)$+nL)) | Exact | Deterministic |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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