The design of variable span linear filters for noise reduction involves a generalized eigenvalue decomposition problem that is of high computational complexity. In order to address this issue, this work proposes a recursive algorithm that computes the filter weights with streaming signal data. Specifically, the inverse square root of the noise covariance matrix is recursively computed with a rank-one update strategy, and the generalized eigenvalues and eigenvectors are approached with the projection approximation subspace tracking method. Numerical simulations show that the proposed recursive method is able to achieve satisfactory performance with significantly lower complexity as compared to the batch algorithm.