Eigenpair closest to mu (Eigenvalues (Iterative Methods))

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Description

Given an n×n matrix A, find the eigenpair (eigenvalue and associated eigenvector) of A with the eigenvalue closest to μ.

Related Problems

Generalizations: Any Eigenpair

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

Parameters

No parameters found.

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Inverse iteration 1921 O(n2) O(n2) Exact Deterministic Time
LOBPCG algorithm 1948 O(n2) O(n)? Exact Deterministic
Homotopy method 1992 O(n2) O(n2)?? Exact Deterministic Time
Folded spectrum method 1934 O(n2) O(n)? Exact Deterministic Time

Time Complexity Graph

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

Space Complexity Graph

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

Time-Space Tradeoff

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