Chebyshev iteration procedure

Propagation of Real Wave Packet with Chebyshev Iteration Procedure... 

The solution to the mapped Schrodinger equation is achieved by a Chebyshev iteration procedure with only the real part of the initial wave packet being involved (note here that the imaginary part of the wave packet is used only once in the first iteration to obtain, ( = r) (z= l,n)) ... 

Equation (11) represents the first iteration of the RWP idea, but it is not the most efficient. It also represents the first appearance of the damping procedure as used in Mandelshtam and Taylor s Chebyshev iteration [4]. 

On computational stability of iterative methods. Until recent years the iterative method with optimal set of Chebyshev s parameters was of little use in numerical solution of grid equations. This can be explained by real facts that various sequences turn out to be nonequivalent in computational procedures. 

A slight variation of this procedure is known as Chebyshev acceleration of SOR and consists of implementing the SOR procedure in two passes, one over the odd matrix elements and one over the even matrix elements with a modification to Eq. (12.76) for the first pass The resulting iterative expressions being ... 

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