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math.NA2026
Average block nonlinear Kaczmarz methods with adaptive momentum for nonlinear systems of equations
Renjie Ding, Dongling Wang, Jun Zou
The Kaczmarz method is widely recognized as an efficient iterative algorithm for solving large-scale linear systems, owing to its simplicity and low memory requirements. However, t…
math.NA2026
Preserving Conservation Laws in the Time-Evolving Natural Gradient Method via Relaxation and Projection Techniques
Zihao Shi, Dongling Wang
Neural networks have demonstrated significant potential in solving partial differential equations (PDEs). While global approaches such as Physics-Informed Neural Networks (PINNs) o…
math.NA2024
Asymptotic stability of many numerical schemes for phase-field modeling
Pansheng Li, Dongling Wang
In the recent breakthrough work \cite{xu2023lack}, a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from…