Need to solve nonlinear systems of equations? This paper introduces HOMPACK, a collection of three algorithms for tracking homotopy zero curves. These algorithms offer global convergence from almost all starting points, providing robust solutions for complex problems. The algorithms leverage ordinary differential equations, normal flow, and augmented Jacobian matrices to trace the homotopy zero curve. Separate routines are available for dense and sparse Jacobian matrices, optimizing performance for different problem structures. HOMPACK includes a high-level driver for polynomial systems, simplifying the application of these advanced techniques. This tool is valuable for researchers and practitioners in mathematics, engineering, and computer science. This research utilizes **mathematical modeling** and the application of **probability** to increase the power of HOMPACK.
As a publication in ACM Transactions on Mathematical Software, this paper aligns perfectly with the journal's focus on algorithms and software for mathematical problems. The introduction of HOMPACK, a software package for tracking homotopy zero curves, contributes directly to the journal's emphasis on practical and efficient mathematical software.