## 6. ConclusionsWe have investigated the feasibility of preprocessing a set of
solar mean multiplet frequencies before performing inversions for
solar structure. This is achieved through forming a linear combination
of the original data, with weights obtained from a singular value
decomposition of a discretized form of the inverse problem. The
inversion is then carried out on only those combinations of modes
which correspond to the largest singular values. This enables a
reduction of the computational time required for the inversion by a
substantial factor - for inversion with optimally localized averages
the reduction factor is of the order , where
The properties of the singular values and associated singular vectors are related to the information content and other aspects of the inverse problem under consideration. For the simple case of rotational inversion in one dimension this was explored in detail by Christensen-Dalsgaard et al. (1993). We have considered a few features of the considerably richer problem of structure inversion, but more detailed investigations of this nature are evidently required. Such investigations would contribute to improving further the efficiency of the inversion procedures, and might provide a deeper insight into the information contents of inversions using different combinations of variables. However, the present investigation has already demonstrated the considerable gain in computational efficiency that can be achieved with SVD preprocessing. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |