Iterative methods for computing the nonlinear Moore–Penrose metric generalized inverse of Banach space operators: convergence, error bounds, and applications

Key Points

• Moore-Penrose inverses can be computed iteratively, showing improved convergence properties.
• The convergence rates are enhanced under specific assumptions on Banach space operators, with established error bounds.
• Analysis of applications illustrates the practical relevance of these methods in operator theory and functional analysis.
• Highlighting the need for further exploration of error bounds in more complex scenarios may enable future advancements.