LANCZOSTHR: Difference between revisions

Latest revision as of 15:25, 18 December 2024

LANCZOSTHR = [real]
Default: LANCZOSTHR = $10^{-3}$

Description: LANCZOSTHR is used by the BSE Lanczos algorithm to stop the iterative procedure, once the dielectric function has reached numerical convergence.

The difference between the dielectric function at two consecutive iterations, $i$ and $i+1$ , is computed as root-mean-square over the frequency grid

{\displaystyle \mathrm{RMS}[\epsilon] = \sqrt{\sum_{j=1}^N\frac{1}{N}\left[\epsilon_{i}(\omega_j)-\epsilon_{i+1}(\omega_j)\right]^2} }

and once $\mathrm{RMS}[\epsilon]<=$ LANCZOSTHR the iterative algorithm stops.

@@ Line 1: / Line 1: @@
-{TAGDEF|LANCZOSTHR|[real]}}
+{{TAGDEF|LANCZOSTHR|[real]|<math>10^{-3}</math>}}
-{{DEF|LANCZOSTHR| <math>10^{-3}</math> | }}
 Description: {{TAG|LANCZOSTHR}} is used by the BSE Lanczos algorithm to stop the iterative procedure, once the dielectric function has reached numerical convergence.
-The difference between the dielectric function at two consecutive iterations, <math>i</math> and <math>i+1</math> is computed as root-mean-square over the frequency grid sampling
+The difference between the dielectric function at two consecutive iterations, <math>i</math> and <math>i+1</math>, is computed as root-mean-square over the frequency grid
 ::<math>
-\mathrm{RMS}[\epsilon] = \sqrt{\sum_{j=1}^N\left[\epsilon_{i}(\omega_j)-\epsilon_{i+1}(\omega_j)\right]^2}
+\mathrm{RMS}[\epsilon] = \sqrt{\sum_{j=1}^N\frac{1}{N}\left[\epsilon_{i}(\omega_j)-\epsilon_{i+1}(\omega_j)\right]^2}
 </math>
-and once <math>\mathrm{RMS}[\epsilon]<=</math>LANCZOSTHR the iterative procedure stops.
+and once <math>\mathrm{RMS}[\epsilon]<=</math>LANCZOSTHR the iterative algorithm stops.
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