Non-Definite, Symmetric Matrix: Difference between revisions
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| [[Gaussian-Jordan Elimination (General Linear System; Positive Definite, Hermitian Matrix; Non-Definite, Symmetric Matrix; Toeplitz Matrix; Vandermonde Matrix Linear System)|Gaussian-Jordan Elimination]] || -150 || $O(n^{3})$ || $O(n^{2})$ || Exact || Deterministic || | |||
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| [[Aasen's method (Non-Definite, Symmetric Matrix Linear System)|Aasen's method]] || 1971 || $O(n^{3})$ || $O(n^{2})$ total || Exact || Deterministic || [https://link-springer-com.ezproxy.canberra.edu.au/article/10.1007/BF01931804 Time] | | [[Aasen's method (Non-Definite, Symmetric Matrix Linear System)|Aasen's method]] || 1971 || $O(n^{3})$ || $O(n^{2})$ total || Exact || Deterministic || [https://link-springer-com.ezproxy.canberra.edu.au/article/10.1007/BF01931804 Time] | ||
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|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Linear System - Non-Definite, Symmetric Matrix - Time.png|1000px]] | [[File:Linear System - Non-Definite, Symmetric Matrix - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Linear System - Non-Definite, Symmetric Matrix - Space.png|1000px]] | [[File:Linear System - Non-Definite, Symmetric Matrix - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Linear System - Non-Definite, Symmetric Matrix - Pareto Frontier.png|1000px]] | [[File:Linear System - Non-Definite, Symmetric Matrix - Pareto Frontier.png|1000px]] | ||
Revision as of 14:04, 15 February 2023
Description
In this case, we restrict $A$ to be non-definite and symmetric.
Related Problems
Generalizations: General Linear System
Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Toeplitz Matrix, Vandermonde Matrix
Parameters
n: number of variables and number of equations
m: number of nonzero entries in matrix
k: ratio between largest and smallest eigenvalues
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Gaussian-Jordan Elimination | -150 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic | |
| Aasen's method | 1971 | $O(n^{3})$ | $O(n^{2})$ total | Exact | Deterministic | Time |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
