Eigenpair with the Largest Eigenvalue (Eigenvalues (Iterative Methods))

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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


$n$: 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

Eigenvalues (Iterative Methods) - Eigenpair with the Largest Eigenvalue - Time.png