Eigenpair with the Largest Eigenvalue (Eigenvalues (Iterative Methods))
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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
$n$: dimension of matrix
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)
Time-Space Tradeoff
_-_Eigenpair_with_the_Largest_Eigenvalue_-_Pareto_Frontier.png)