On the Numerical Stability of Fourier Extensions

@article{Adcock2014OnTN,
  title={On the Numerical Stability of Fourier Extensions},
  author={B. Adcock and D. Huybrechs and J. Mart{\'i}n-Vaquero},
  journal={Foundations of Computational Mathematics},
  year={2014},
  volume={14},
  pages={635-687}
}
  • B. Adcock, D. Huybrechs, J. Martín-Vaquero
  • Published 2014
  • Computer Science, Mathematics
  • Foundations of Computational Mathematics
  • An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect such rapid convergence to be destroyed when carrying out computations in finite precision. The purpose… CONTINUE READING
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