Linear inversions for the Sun's internal rotation

Interesting inversion problems arise in helioseismology, the seismic study of the interior of the Sun using the frequencies of its global resonant modes of oscillation. In particular, one can use the frequencies to investigate how the rotation of the Sun varies beneath the visible surface. This review concentrates primarily on the methods and tools that have been used in the helioseismic inversion problem. In particular, an analysis of different inversion methods using the spectral properties of a generalized singular-value decomposition has proved useful in helioseismology, and this suggests ways in which the inversion of large datasets can be performed more efficiently.