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 [146], and implemented by Ashby [7].
Chebyshev iteration is suitable for any nonsymmetric linear system for
which the enveloping ellipse does not include the origin.