Chebyshev Iteration is another method for solving nonsymmetric problems (see Golub and Van Loan [.1.5]GoVL:matcomp and Varga [Chapter 5]Va:book). Chebyshev Iteration avoids the computation of inner products as is necessary for the other nonstationary methods. For some distributed memory architectures these inner products are a bottleneck with respect to efficiency. The price one pays for avoiding inner products is that the method requires enough knowledge about the spectrum of the coefficient matrix that an ellipse enveloping the spectrum can be identified ; however this difficulty can be overcome via an adaptive construction developed by Manteuffel , and implemented by Ashby . Chebyshev iteration is suitable for any nonsymmetric linear system for which the enveloping ellipse does not include the origin.