Information-based complexity of linear operator equations

@article{Nemirovsky1992InformationbasedCO,
  title={Information-based complexity of linear operator equations},
  author={A. S. Nemirovsky},
  journal={J. Complexity},
  year={1992},
  volume={8},
  pages={153-175}
}
x being the unknown. Assume that, given an instance (A, b), we wish to solve it to a given accuracy E on the basis of “matrix-vector mu ltiplications.” More precisely, assume that we are given b beforehand, and the only source of information about A is the oracle 0 which transforms a given input u E H into the pair (Ax, A*$, where A* is the operator conjugate to A. The problem is to evaluate the complexity of solving the equation to a given accuracy, i.e., given a class 2l of instances, to… CONTINUE READING