Author: bugman
Date: Thu Aug 30 11:02:04 2012
New Revision: 17391
URL: http://svn.gna.org/viewcvs/relax?rev=17391&view=rev
Log:
Added a paragraph to the model-free chapter of the user manual explaining the
J(w) equation forms.
Modified:
trunk/docs/latex/model-free.tex
Modified: trunk/docs/latex/model-free.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/model-free.tex?rev=17391&r1=17390&r2=17391&view=diff
==============================================================================
--- trunk/docs/latex/model-free.tex (original)
+++ trunk/docs/latex/model-free.tex Thu Aug 30 11:02:04 2012
@@ -118,6 +118,7 @@
\noindent where $S^2_f$ and $\tau_f$ are the amplitude and timescale of the
faster of the two motions whereas $S^2_s$ and $\tau_s$ are those of the
slower motion. $S^2_f$ and $S^2_s$ are related by the formula $S^2 = S^2_f
\cdot S^2_s$.
+If these forms of the model-free spectral density functions are unfamiliar,
that is because these are the numerically stabilised forms presented in
\citet{dAuvergneGooley08a}. The original model-free spectral density
functions presented in \inlinecite{LipariSzabo82a} and \inlinecite{Clore90a}
are not the most numerically stable form of these equations. An important
problem encountered in optimisation is round-off error in which machine
precision influences the result of mathematical operations. The double
reciprocal $\tau^{-1} = \tau_m^{-1} + \tau_e^{-1}$ used in the equations are
operations which are particularly susceptible to round-off error, especially
when $\tau_e \ll \tau_m$. By incorporating these reciprocals into the
model-free spectral density functions and then simplifying the equations this
source of round-off error can be eliminated, giving relax an edge over other
model-free optimisation softwares.
% Brownian rotational diffusion.
r17391 - /trunk/docs/latex/model-free.tex