= Skew-tridiagonal Jacobi and Gauss-Seidel iterations
For $A=\mu^{-1}I+U-U^T$, with $U$ the four-dimensional unit superdiagonal, the <Jacobi method> has eigenvalues $2i\mu\cos(j\pi/5)$, $j=1,\ldots,4$. The <Gauss-Seidel method> has two zero eigenvalues and $-\mu^2(3\pm\sqrt5)/2$. Therefore both methods converge for every starting vector exactly when $0<|\mu|<(\sqrt5-1)/2$. This equality of convergence ranges follows from their spectra, not from positive-definiteness of the nonsymmetric coefficient matrix.
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