Eigenpair closest to mu (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 eigenvalue closest to $\mu$.

Related Problems

Generalizations: Any Eigenpair

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


$n$: 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

Eigenvalues (Iterative Methods) - Eigenpair closest to mu - Time.png