= Richardson iteration
{c}
{title2=$x_{n+1}=x_n-\tau(Ax_n-b)$}
For a real symmetric positive definite <matrix> $A$, the error in each <eigenvector> direction is multiplied by $1-\tau\lambda$. Convergence from every initial vector is therefore equivalent to $0<\tau<2/\lambda_{\max}$. At either endpoint there is a nondecaying error direction. The optimal constant parameter is $2/(\lambda_{\min}+\lambda_{\max})$, giving contraction factor $(\lambda_{\max}-\lambda_{\min})/(\lambda_{\max}+\lambda_{\min})$.
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