**AAS Meeting #194 - Chicago, Illinois, May/June 1999**

*Session 93. Quiet Photosphere, Chromosphere and Transition Region*

Display, Thursday, June 3, 1999, 9:20am-4:00pm, Southeast Exhibit Hall
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## [93.13] Preconditioning the DEM(T) inverse problem

*P. Charbonneau, S. McIntosh (HAO/NCAR)*

In an inverse problem of any kind, poor conditioning of the
inverse operator decreases the numerical stability of any
unregularized solution in the presence of data noise. In
this poster we show that the numerical stability of the
differential emission measure (DEM) inverse problem can be
considreably improved by judicious choice of the integral
operator. Specifically, we formulate a combinatorial
optimization problem where, in a preconditioning step, a
subset of spectral lines is selected in order to minimize
the condition number of the discretized integral operator.
This turns out to be a hard combinatorial optimization
problem, which we tackle using a genetic algorithm.

We apply the technique to the dataset comprising the solar
UV/EUV emission lines in the SOHO SUMER/CDS wavelength
range, and to the Harvard S-055 EUV spectroheliometer data.
The temperature distribution in the emitting region of the
solar atmosphere is recovered with considerably better
stability and smaller error bars when our preconditioning
technique is used, even though this involves the analysis of
*fewer* spectral lines than in the conventional
``all-lines'' approach.

If the author provided an email address or URL for general inquiries, it is a
s follows:

paulchar@ncar.ucar.edu

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