Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers

  title={Tractability of Approximation 
for Weighted Korobov Spaces
on Classical and Quantum Computers},
  author={Erich Novak and Ian H. Sloan and Henryk Wozniakowski},
  journal={Foundations of Computational Mathematics},
Abstract We study the approximation problem (or problem of optimal recovery in the $L_2$-norm) for weighted Korobov spaces with smoothness parameter $\a$. The weights $\gamma_j$ of the Korobov spaces moderate the behavior of periodic functions with respect to successive variables. The nonnegative smoothness parameter $\a$ measures the decay of Fourier coefficients. For $\a=0$, the Korobov space is the $L_2$ space, whereas for positive $\a$, the Korobov space is a space of periodic functions… 


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