On the Convergence of Newton’s Method Combined With a Proximal Approach for an Eigenvalue Problem - A Corrected Version

Key Points

• The convergence of the numerical method was established using the Banach fixed point theorem, confirming its validity.
• A specific numerical example was provided for a Ginzburg-Landau type equation, showcasing practical application.
• We developed software that implements this numerical method for solving eigenvalue problems effectively.
• This research highlights the potential of combining Newton's method with proximal approaches for efficient problem-solving.