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Here the results of the presmoother on the finest level are analyzed by Fourier techniques.

The Fourier decomposition of the initial error (that is the initial values minus the true solution) is represented by

In this chart each bar represents the magnitude of a Fourier coefficient of the decomposition of the error in a series of the form

After two smoothing steps, the error becomes in the same representation

Clearly, the high frequency error components have been reduced nicely, while the low frequency components have stayed almost untouched.

Ulrich Ruede , Thu Feb 2 21:06:49 MEZ 1995

Updated by Craig C. Douglas