Eigenpair with the Largest Eigenvalue: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Eigenpair with the Largest Eigenvalue (Eigenvalues (Iterative Methods))}} == Description == Given an $n \times n$ matrix $A$, find the eigenpair (eigenvalue and associated eigenvector) of $A$ with the largest eigenvalue. == Related Problems == Generalizations: Any Eigenpair Related: All Eigenvalues, Any Eigenvalue, All Eigenpairs, Eigenpair closest to mu == Parameters == No parameters found. == Table of Algorithms == {| clas...") |
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Time.png|1000px]] | [[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Space.png|1000px]] | [[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Pareto Frontier.png|1000px]] | [[File:Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Pareto Frontier.png|1000px]] | ||
Revision as of 14:04, 15 February 2023
Description
Given an $n \times n$ matrix $A$, find the eigenpair (eigenvalue and associated eigenvector) of $A$ with the largest eigenvalue.
Related Problems
Generalizations: Any Eigenpair
Related: All Eigenvalues, Any Eigenvalue, All Eigenpairs, Eigenpair closest to mu
Parameters
No parameters found.
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Power Iteration | 1929 | $O(n^{2})$ | $O(n)$ | Exact | Deterministic | Time |
Time Complexity Graph
_-_Eigenpair_with_the_Largest_Eigenvalue_-_Time.png)
Space Complexity Graph
_-_Eigenpair_with_the_Largest_Eigenvalue_-_Space.png)
Pareto Frontier Improvements Graph
_-_Eigenpair_with_the_Largest_Eigenvalue_-_Pareto_Frontier.png)