Classical and Quantum Complexity of the Sturm–Liouville Eigenvalue Problem

@article{Papageorgiou2005ClassicalAQ,
  title={Classical and Quantum Complexity of the Sturm–Liouville Eigenvalue Problem},
  author={Anargyros Papageorgiou and Henryk Wozniakowski},
  journal={Quantum Information Processing},
  year={2005},
  volume={4},
  pages={87-127}
}
We study the approximation of the smallest eigenvalue of a Sturm–Liouville problem in the classical and quantum settings. We consider a univariate Sturm–Liouville eigenvalue problem with a nonnegative function q from the class C2 ([0,1]) and study the minimal number n(ɛ) of function evaluations or queries that are necessary to compute an ɛ-approximation of the smallest eigenvalue. We prove that n(ɛ)=Θ(ɛ−1/2) in the (deterministic) worst case setting, and n(ɛ)=Θ(ɛ−2/5) in the randomized setting… 

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