We present an efficient method for two dimensional inversions for the solar
rotation rate using the Subtractive Optimally Localized Averages (SOLA) method
and a modification of the R1 X R1 technique proposed by Sekii (1993). The SOLA
method is based on explicit construction of averaging kernels similar to the
Backus-Gilbert method. The versatility and reliability of the SOLA method in
reproducing a target form for the averaging kernel, in combination with the
idea of the R1 X R1 decomposition, results in a computationally very efficient
inversion algorithm. This is particularly important for full 2-D inversions of
helioseismic data in which the number of modes runs into at least tens of
thousands.Comment: 12 pages, Plain TeX + epsf.tex + mn.te