Convergence frontier analysis of sparse-matrix quasi-Newton methods: applications to rock blasting geomechanics

Abstract

We delimit the convergence frontier of sparse–matrix quasi-Newton algorithms for rock-blasting simulations. Lip- schitz/Hölder bounds yield Kantorovich radii that mark when the secant matrix preserves contraction. A limited- memory BFGS with adaptive switching to full Newton is introduced as the frontier is approached. A synthetic dataset of 25 000 cases, calibrated with limestone, copper and iron mines, reveals a 35 % larger convergence radius and a three-order reduction in runtime versus dense Newton. The iterative map exposes fragile-fracture regions, providing a preventive rule for drill-pattern and charge design. The results bridge nonlinear analysis with field practice, enabling stable, scalable HPC simulations for modern blast-engineering workflows.