Adaptive spline interpolation for Hamilton–Jacobi–Bellman equations
Copyright policy )Adaptive spline interpolation for Hamilton–Jacobi–Bellman equations
We study the performace of adaptive spline interpolation in semi--Lagrangian discretization schemes for Hamilton--Jacobi--Bellman equations. We investigate the local approximation properties of cubic splines on locally refined grids by a theoretical analysis. Numerical examples show how this method performs in practice. Using those examples we also illustrate numerical stability issues.
- New School United States
- University of Bayreuth Germany
viscosity solution, Numerical optimization and variational techniques, spline interpolation, convergence, Discrete approximations in optimal control, Viscosity solution, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, Numerical stability, 500, Adaptive discretization, Optimal control, Adaptive grids, 510, adaptive grids, fixed point equation, optimal control, numerical example, numerical stability, Numerical example, Fixed point equation, Spline interpolation, Convergence, adaptive discretization
viscosity solution, Numerical optimization and variational techniques, spline interpolation, convergence, Discrete approximations in optimal control, Viscosity solution, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, Numerical stability, 500, Adaptive discretization, Optimal control, Adaptive grids, 510, adaptive grids, fixed point equation, optimal control, numerical example, numerical stability, Numerical example, Fixed point equation, Spline interpolation, Convergence, adaptive discretization
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