A low-storage filter diagonalization method for quantum eigenenergy calculation or for spectral analysis of time signals

1997 ◽  
Vol 106 (12) ◽  
pp. 5085-5090 ◽  
Author(s):  
Vladimir A. Mandelshtam ◽  
Howard S. Taylor
Keyword(s):  
Spectral Analysis ◽  
Filter Diagonalization ◽  
Time Signals ◽  
Diagonalization Method ◽  
Filter Diagonalization Method

ON HARMONIC INVERSION OF CROSS-CORRELATION FUNCTIONS BY THE FILTER DIAGONALIZATION METHOD

2003 ◽  
Vol 02 (04) ◽  
pp. 497-505 ◽  
Author(s):  
VLADIMIR A. MANDELSHTAM
Keyword(s):  
Correlation Functions ◽  
Cross Correlation ◽  
Window Size ◽  
Initial State ◽  
Filter Diagonalization ◽  
Molecular Systems ◽  
Diagonalization Method ◽  
Low Dimensional ◽  
Harmonic Inversion ◽  
Filter Diagonalization Method

Harmonic inversion of Chebyshev correlation and cross-correlation functions by the filter diagonalization method (FDM) is one of the most efficient ways to accurately compute the complex spectra of low dimensional quantum molecular systems. This explains the growing popularity of the FDM in the past several years. Some of its most attractive features are the predictable convergence properties and the lack of adjusting parameters. These issues however are often misunderstood and mystified. We discuss the questions relevant to the optimal choices for the FDM parameters, such as the window size and the number of basis functions. We also demonstrate that the cross-correlation approach (using multiple initial states) is significantly more effective than the conventional autocorrelation approach (single initial state) for the common case of a non-uniform eigenvalue distribution.

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