Efficient recursive least squares solver for rank-deficient matrices - HAL_CHIMIE_ENSLYON Accéder directement au contenu
Article Dans Une Revue Applied Mathematics and Computation Année : 2021

Efficient recursive least squares solver for rank-deficient matrices

Résumé

Updating a linear least squares solution can be critical for near real-time signalprocessing applications. The Greville algorithm proposes a simple formula for updating the pseudoinverse of a matrix A ∈ R n×m with rank r. In this paper, we explicitly derive a similar formula by maintaining a general rank factorization, which we call rank-Greville. Based on this formula, we implemented a recursive least squares algorithm exploiting the rank-deficiency of A, achieving the update of the minimum-norm least-squares solution in O(mr) operations and, therefore, solving the linear least-squares problem from scratch in O(nmr) operations. We empirically confirmed that this algorithm displays a better asymptotic time complexity than LAPACK solvers for rank-deficient matrices. The numerical stability of rank-Greville was found to be comparable to Cholesky-based solvers. Nonetheless, our implementation supports exact numerical representations of rationals, due to its remarkable algebraic simplicity.
Fichier principal
Vignette du fichier
article_draft.pdf (626.87 Ko) Télécharger le fichier

Dates et versions

hal-03254881 , version 1 (21-06-2021)

Identifiants

Citer

Ruben Staub, Stephan N. Steinmann. Efficient recursive least squares solver for rank-deficient matrices. Applied Mathematics and Computation, 2021, 399, pp.125996. ⟨10.1016/j.amc.2021.125996⟩. ⟨hal-03254881⟩
73 Consultations
242 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More