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With Fourier analysis we find a method of spectral factorization
that is as fast as Fourier transformation,
namely
for a matrix of size N.
This is very appealing.
An earlier
version of this book included such an algorithm.
Pedagogically, I didn't like it in this book because it
requires lengthy off-topic discussions of Fourier analysis
which are already found in both my first book FGDP and my third book PVI.
The weakness of the Kolmogoroff method is related to its strength.
Fourier methods strictly require the matrix to be a band matrix.
A matrix that is ``almost'' a band matrix adds complexity beyond
my textbooks.
Next: WILSON-BURG SPECTRAL FACTORIZATION
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Previous: Toeplitz methods
Stanford Exploration Project
12/15/2000