Take the z-transform of (6.2.6) and show that Xz_ _
Chapter , Problem 6.16(choose chapter or problem)
Take the z-transform of (6.2.6) and show that Xz_ _ Gz_Yz_, where Gz_ _ zU ? M_ ?1 D?1 and U is the unit matrix. Gz_ is the matrix transfer function of a digital filter that represents the Jacobi or GaussSeidel methods. The filter poles are obtained by solving detzU ? M_ _ 0. The filter is stable if and only if all the poles have magnitudes less than 1.
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