NonlinearSolvejl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
<|reference_start|>NonlinearSolvejl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia: Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex system models remains a challenge. This paper presents NonlinearSolve.jl - a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for GPU-accelerated computation through static array kernels, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as Sundials and MINPACK, NonlinearSolve.jl demonstrates unparalleled robustness and efficiency, achieving significant advancements in solving benchmark problems and challenging real-world applications. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.<|reference_end|>
@article{pal2024nonlinearsolve.jl:,
    title={NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of
  Nonlinear Equations in Julia},
    author={Avik Pal, Flemming Holtorf, Axel Larsson, Torkel Loman, Utkarsh, Frank
  Sch"aefer, Qingyu Qu, Alan Edelman, Chris Rackauckas},
    journal={arXiv preprint arXiv:2403.16341},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16341},
    primaryClass={math.NA cs.NA}
}