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math.OC2025
Mini-Extragradient Methods
Xiaozhi Liu, Yong Xia
The Extragradient (EG) method stands as a cornerstone algorithm for solving monotone nonlinear equations but faces two important unresolved challenges: (i) how to select stepsizes…
math.OC2025
Split-Merge Revisited: A Scalable Approach to Generalized Eigenvalue Problems
Xiaozhi Liu, Yong Xia
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approach…
math.OC2025
Split-Merge: A Difference-based Approach for Dominant Eigenvalue Problem
Xiaozhi Liu, Mengmeng Song, Yong Xia
The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Ra…