Spectral Analysis of Nonlinear Operators: Theory and Applications to Neural Networks and Optimization
Archives of Current Research International · pp. 287–295 · Published 12 Jun 2025
10.9734/acri/2025/v25i61272Abstract
This paper presents a nonlinear spectral framework for analyzing monotone and nonexpansive operators in Banach and Hilbert spaces. We construct a nonlinear spectral resolution for maximal monotone operators using Yosida approximations and Fitzpatrick functions, leading to a family of nonlinear projections and an associated spectral measure. For nonexpansive mappings, we establish an iterative spectral approximation based on Krasnoselskii iterations, with proven convergence and recovery of nonlinear eigenvectors. We further extend this framework to ReLU-based neural networks, analyzing spectral bounds, depth-dependent scaling, and gradient alignment. These results bridge nonlinear operator theory and neural architectures, offering new tools for theoretical analysis and applications in optimization, physics, and machine learning.
Cited by 0
No indexed citations yet.
Related research
- Assessment of Global Solar Radiation at Selected Points in Nigeria Using Artificial Neural Network Model (ANNM) — shares topic coverage
- Technologies in Texture Analysis – A Review — shares topic coverage
- Evaluation of Plastic Waste Classification Systems — shares topic coverage
- Application of Neural Networks for Predicting the Workability of Self-Compacting Concrete — shares topic coverage
- Review of Neural Network Algorithm and its Application in Temperature Control of Distillation Tower — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
0
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.