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How is an exact bound on estimated error of an iterative algorithm related to rate of convergence?

Referring to references is appreciated. Edit: Now I am not talking about any bound. I am only talking about exact bounds.

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  • $\begingroup$ You need to narrow the scope of your question significantly. There are simply too many algorithms, pessimistic error bounds, and extremely accurate error estimates to chose from. $\endgroup$ – Carl Christian Feb 13 '16 at 22:49
  • $\begingroup$ I am sorry, but I still do not understand you question. Error bounds are typically pessimistic but tend to accurately predict the asymptotic rate of convergence. I am aware of exactly one example where there is cubic convergence in practice, but the (current) theory only predicts quadratic convergence. Precise error estimates are typically constructed by exploiting some property of the algorithm or the problem, but are not necessarily tied to the rate of convergence. $\endgroup$ – Carl Christian Feb 19 '16 at 11:12

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