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The problem of estimating the errors arising in a variety of numerical operations involving bandlimited functions is considered. The errors are viewed as responses of suitably created systems, and the analysis is based on the evaluation of the maximum response of these systems in terms of the energy or power of their input. The investigation includes deterministic and random signals, and it is extended to two-dimensional functions and Hankel transforms. Finally, the results are related to the uncertainty principle in one and two variables.