Runge–Kutta integrators yield optimal regularization schemes

@article{Rieder2005RungeKuttaIY,
  title={Runge–Kutta integrators yield optimal regularization schemes},
  author={Andreas Rieder},
  journal={Inverse Problems},
  year={2005},
  volume={21},
  pages={453 - 471}
}
  • A. Rieder
  • Published 1 April 2005
  • Mathematics
  • Inverse Problems
Asymptotic regularization (also called Showalter's method) is a theoretically appealing regularization scheme for an ill-posed problem Tx = y, T acting between Hilbert spaces. Here, Tx = y is stably solved by evaluating the solution of the evolution equation u′(t) = T*(y − Tu(t)), u(0) = 0, at a properly chosen finite time. For a numerical realization, however, we have to apply an integrator to the ODE. Fortunately all properties of asymptotic regularization carry over to its numerical… 
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