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Kolmogoroff spectral factorization

With Fourier analysis we find a method of spectral factorization that is as fast as Fourier transformation, namely $N\log N$ 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 up previous print clean
Next: WILSON-BURG SPECTRAL FACTORIZATION Up: SPECTRAL FACTORIZATION Previous: Toeplitz methods
Stanford Exploration Project
12/15/2000