Chebyshev semi-iterative method

It is natural to ask how this Chebyshev semi-iterative method compares... 

Theorem The successive overrelaxation method with optimum relaxation factor converges at least twice as fast as the Chebyshev semi-iterative method with respect to the Jacobi method, and therefore at least twice as fast as any semi-iterative method with respect to the Jacobi method. Furthermore, as the number of iterations tends to infinity, the successive overrelaxation method becomes exactly twice as fast as the Chebyshev semi-iterative method. 

Added in proof A new iterative method, called the modified Chebyshev semi-itera-live method, eliminated this factor of two in the cyclic case, and is more rapidly convergent than the successive over-relaxation iterative method. See [18a]. 

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