Although the determination of exact eigenvalues and eigenvectors requires considerable computation, the following iterative algorithm converges with reasonable efficiency to the eigenvector that corresponds to the largest eigenvalue:

Assumptions and Notation:

• A is a (non-singular) N × N matrix.
• A has N linearly independent eigenvectors.
• Unit eigenvectors B₁, B₂, ..., B_N have eigenvalues λ₁, λ₂, ..., λ_N.
• The eigenvectors and eigenvalues have been ordered, so that |λ₁| > |λ₂| ≥ ... ≥ |λ_N|
  (Note we assume |λ₁| ≠ |λ₂| .)

created: 10 February 2007 last revised: 15 February 2007

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