Efficient recursive least squares solver for rank-deficient matrices

Updating a linear least squares solution can be critical for near real-time signalprocessing applications. The Greville algorithm proposes simple formula updating the pseudoinverse of matrix A $\in$ R nxm with rank r. In this paper, we explicitly derive similar by maintaining general factorization, which call rank-Greville. Based on formula, implemented recursive exploiting rank-deficiency A, achieving update minimum-norm least-squares in O(mr) operations and, therefore, solving problem from scratch O(nmr) operations. We empirically confirmed that displays better asymptotic time complexity than LAPACK solvers rank-deficient matrices. numerical stability rank-Greville was found to comparable Cholesky-based solvers. Nonetheless, our implementation supports exact representations rationals, due its remarkable algebraic simplicity.