Abstract
Abstract Hamilton–Jacobi equations are a type of nonlinear hyperbolic partial differential equations that arise in many applications such as optimal control, game theory, moving interface problems, geophysics and seismology, computer vision and image processing. The fast sweeping method (FSM) is a simple and efficient iterative numerical method that can achieve optimal complexity for solving stationary convex Hamilton–Jacobi equations. In this chapter, we will give a brief survey on the FSM, its modification/extension to more general hyperbolic problems and its many successful applications in geophysics, optimal control, image processing and computer vision.
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