The real-number model of computation is used in computational geometry, in the approach suggested by Blum, Shub, and Smale and in information based complexity.
In this paper we propose a refinement of this model, the TTE-model of computation. In contrast to the real-number model, which is unrealistic or at least too optimistic, the TTE-model is very realistic; i.e., for TTE-algorithms there are digital computers, which behave exactly the same way as predicted by the theoretical model. We start with a detailed discussion of some objections to the real-number model. We introduce the refined model by adding the condition "every partial input or output information of an algorithm is finite" to the assumptions of the IBC-model of computation. First, we explain computability and computational complexity in TTE for the simple case of real functions. Then we apply the refined model to two typical IBC-problems, integration and zero-finding on the space C [0; 1] of continuous real functions. We study computability and computational complexity and compare TTE-results with IBC-results. Finally, we briefly discuss the computation of discontinuous problems. This paper does not present new technical results but should be considered as a fresh impetus to reflect on models of computation for numerical analysis and as an invitation to try out the TTE-model of computation in information based complexity.