2012/09/24 by Jennifer B. Erway, Erway, Jennifer B., Vibhor Jain +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1209.5141
openalex publication_date 2012/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate fast direct methods for solving systems of the form (B + G)x = y, where B is a limited-memory BFGS matrix and G is a symmetric positive-definite matrix. These systems, which we refer to as shifted L-BFGS systems, arise in several settings, including trust-region methods and preconditioning techniques for interior-point methods. We show that under mild assumptions, the system (B + G)x = y can be solved in an efficient and stable manner via a recursion that requies only vector inner products. We consider various shift matrices G and demonstrate the effectiveness of the recursion methods in numerical experiments.