Matrix A (2×2)
Iteration: 0
λ estimate: —
True λ₁: —
|error|: —
Ratio λ₂/λ₁: —
Power iteration: vₙ = Avₙ₋₁ / ‖Avₙ₋₁‖. Converges to dominant eigenvector with rate |λ₂/λ₁|ⁿ.
Rayleigh quotient: λ ≈ vᵀAv / vᵀv — best eigenvalue estimate from eigenvector.
Convergence: geometric with ratio r = |λ₂/λ₁| — faster when eigenvalues are well-separated.
Circle: shows unit circle with current vector (cyan) converging to true eigenvector (green).
Bottom: convergence of |λ estimate − λ true| — log scale shows linear convergence (geometric rate).
Rayleigh quotient: λ ≈ vᵀAv / vᵀv — best eigenvalue estimate from eigenvector.
Convergence: geometric with ratio r = |λ₂/λ₁| — faster when eigenvalues are well-separated.
Circle: shows unit circle with current vector (cyan) converging to true eigenvector (green).
Bottom: convergence of |λ estimate − λ true| — log scale shows linear convergence (geometric rate).