One common procedure in the solution of a normalized damped linear system with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, if the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error bound.

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