In this paper, we consider the problem of tracking the signal subspace under a sparsity constraint on the weight basis matrix. In the same spirit of our previous work, we propose a new low cost algorithm based on a two stages approach. First, an orthogonal basis of the signal subspace is estimated adaptively. Then, a sparsity criterion is minimized using the Shear and Givens rotations. Compared to [3], we propose to use Taylor expansion and Newton descent method to accelerate the optimization. The proposed algorithm has approximately the same estimation and tracking performance as compared to our previous propositions [2], [3] but with the advantage of a lower computational cost.