Iterative Method Convergence

Numerical Analysis · Axiom Academy

LESSON Iterative Method Convergence Understanding when and how fast iterations converge For any iteration x⁽ᵏ⁺¹⁾ = Gx⁽ᵏ⁾ + c, convergence depends entirely on the spectral radius of G: The error at iteration k behaves like: The rate of convergence tells us how many iterations to reduce error by factor e: Sufficient Conditions for Convergence Computing ρ(G) directly requires finding eigenvalues—expensive! Instead, we use sufficient conditions: We can't iterate forever! Common stopping criteria: You now understand the theory behind iterative method convergence!

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