Toeplitz Matrix: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 26: | Line 26: | ||
|- | |- | ||
| [[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 || | |||
|- | |||
| [[Levinson–Durbin recursion (Toeplitz Matrix Linear System)|Levinson–Durbin recursion]] || 1947 || $O(n^{2})$ || $O(n^{2})$ total || Exact || Deterministic || [https://onlinelibrary-wiley-com.ezproxy.canberra.edu.au/doi/abs/10.1002/sapm1946251261 Time] | | [[Levinson–Durbin recursion (Toeplitz Matrix Linear System)|Levinson–Durbin recursion]] || 1947 || $O(n^{2})$ || $O(n^{2})$ total || Exact || Deterministic || [https://onlinelibrary-wiley-com.ezproxy.canberra.edu.au/doi/abs/10.1002/sapm1946251261 Time] | ||
|- | |- | ||
| Line 32: | Line 34: | ||
|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Linear System - Toeplitz Matrix - Time.png|1000px]] | [[File:Linear System - Toeplitz Matrix - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Linear System - Toeplitz Matrix - Space.png|1000px]] | [[File:Linear System - Toeplitz Matrix - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Linear System - Toeplitz Matrix - Pareto Frontier.png|1000px]] | [[File:Linear System - Toeplitz Matrix - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
In this case, we restrict $A$ to be a Toeplitz matrix.
Related Problems
Generalizations: General Linear System
Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric 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 | |
| Levinson–Durbin recursion | 1947 | $O(n^{2})$ | $O(n^{2})$ total | Exact | Deterministic | Time |
| Bareiss Algorithm | 1969 | $O(n^{2})$ | $O(n^{2})$ total | Exact | Deterministic | Time |
Time Complexity Graph
Error creating thumbnail: Unable to save thumbnail to destination
Space Complexity Graph
Error creating thumbnail: Unable to save thumbnail to destination
Pareto Frontier Improvements Graph
Error creating thumbnail: Unable to save thumbnail to destination