In this paper, an algebraic characterization is made of the problem of resolving two or more closely spaced (in frequency wave number) plane waves incident on a linear array. This algebraic characterization in turn suggests a number of adaptive procedures for effecting the desired resolution. One of these procedures is herein empirically shown to provide significantly better performance when compared to other contemporary procedures used in array processing such as the Wiener filter, Pisarenko and MLM algorithms. This includes both a better frequency resolving capability and a faster convergence rate.