Eigenpair closest to mu (Eigenvalues (Iterative Methods))

Description

Given an $n \times n$ matrix $A$, find the eigenpair (eigenvalue and associated eigenvector) of $A$ with the eigenvalue closest to $\mu$.

Related Problems

Generalizations: Any Eigenpair

Related: All Eigenvalues, Any Eigenvalue, All Eigenpairs, Eigenpair with the Largest Eigenvalue

Parameters

$n$: dimension of matrix

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Inverse iteration	1921	$O(n^{2})$	$O(n^{2})$	Exact	Deterministic	Time
LOBPCG algorithm	1948	$O(n^{2})$	$O(n)$?	Exact	Deterministic
Homotopy method	1992	$O(n^{2})$	$O(n^{2})$??	Exact	Deterministic	Time
Folded spectrum method	1934	$O(n^{2})$	$O(n)$?	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

Time-Space Tradeoff

Error creating thumbnail: Unable to save thumbnail to destination