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Function parametrization (view source)

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The method of function parameterization (FP) consists of the                  
The method of function parameterization (FP) consists of the numerical determination, by statistical regression on a database of simulated states, of  simple functional representations  
numerical determination,                                                      
of   parameters characterizing the state of a particular physical system, where the arguments of the functions are statistically independent combinations of diagnostic raw measurements of
by statistical regression on a database of                                    
the system whose geometry is fixed.  The technique,  developed by H. Wind for the purpose of momentum determination from spark chamber data
simulated states, of  simple functional representations of                    
parameters characterizing the state of a particular physical                  
system, where                                                                
the arguments of the functions are statistically independent                  
combinations of diagnostic raw measurements                                    
of the system whose geometry is                                                
fixed.  The technique,  developed by H. Wind                                  
for the purpose of momentum determination from spark chamber data              
<ref>    Wind, H.,                                                                 
<ref>    Wind, H.,                                                                 
     `Function Parametrization'                                                 
     `Function Parametrization'                                                 
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finding',  (b) `interpolation and function representation'                   
finding',  (b) `interpolation and function representation'                   
in ``Formulae and Methods in Experimental Data Evaluation'',                     
in ``Formulae and Methods in Experimental Data Evaluation'',                     
Vol.~3, European Physical Society, Geneva, 1984</ref>,
Vol. 3, European Physical Society, Geneva, 1984</ref>, was introduced by B. Braams to plasma physics, where its  first application (to the analysis of equilibrium magnetic  
 
measurements on ASDEX) together with a succinct mathematical description, appeared in ref. <ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref>.  
was                                              
introduced by B. Braams to plasma physics, where its  first                    
application (to the analysis of equilibrium magnetic                          
measurements on ASDEX) together with an admirably succinct                    
mathematical description, appeared in ref. <ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref>.  


The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known.
The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known.
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