Papers › Characterizing GSVD by singular value expansion of linear operators and its computation
Characterizing GSVD by singular value expansion of linear operators and its computation
Haibo Li
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The generalized singular value decomposition (GSVD) of a matrix pair {A, L} with A∈ℝ^(m×n) and L∈ℝ^(p×n) generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we provide a new understanding of GSVD from the viewpoint of SVD, based on which we propose a new iterative method for computing nontrivial GSVD components of a large-scale matrix pair. By introducing two linear operators 𝒜 and ℒ induced by {A, L} between two finite-dimensional Hilbert spaces and applying the theory of singular value expansion (SVE) for linear compact operators, we show that the GSVD of {A, L} is nothing but the SVEs of 𝒜 and ℒ. This result characterizes completely the structure of GSVD for any matrix pair with the same number of columns. As a direct application of this result, we generalize the standard Golub-Kahan bidiagonalization (GKB) that is a basic routine for large-scale SVD computation such that the resulting generalized GKB (gGKB) process can be used to approximate nontrivial extreme GSVD components of {A, L}, which is named the gGKB\_GSVD algorithm. We use the GSVD of {A, L} to study several basic properties of gGKB and also provide preliminary results about convergence and accuracy of gGKB\_GSVD for GSVD computation. Numerical experiments are presented to demonstrate the effectiveness of this method.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections