Square Matrix LU Decomposition: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:LU Decomposition - Square Matrix LU Decomposition - Time.png|1000px]] | [[File:LU Decomposition - Square Matrix LU Decomposition - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:LU Decomposition - Square Matrix LU Decomposition - Space.png|1000px]] | [[File:LU Decomposition - Square Matrix LU Decomposition - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:LU Decomposition - Square Matrix LU Decomposition - Pareto Frontier.png|1000px]] | [[File:LU Decomposition - Square Matrix LU Decomposition - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
Lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. In this specific case, the input is a square $n \times n$ matrix
Related Problems
Generalizations: Rectangular Matrix LU Decomposition
Parameters
$n$: dimension of square matrix
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Doolittle Algorithm | 1878 | $O(n^{3})$ | $\tilde{O}({1})$ | Exact | Deterministic | |
| Crout and LUP algorithms | 2007 | $O(n^{3})$ | $\tilde{O}({1})$ | Exact | Deterministic | Time |
| Okunev; Johnson | 1997 | $O(n^{3})$ | $O({1})$ | Exact | Deterministic | Time |
| Bunch; Hopcroft | 1974 | $O(n^{2.{37}6})$ | $\tilde{O}(n^{2})$ | Exact | Deterministic | Time |
| Closed formula | 1975 | $O(nlogn)$ | Exact | Deterministic | ||
| David | 2006 | $O(nlogn)$ | Exact | Deterministic | ||
| Press, Teukolsky, Flannery | 2007 | $O(n^{3})$ | $\tilde{O}(n)$ | Exact | Deterministic | Time |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
