Why does information-based complexity use the real number model?

Abstract

We explain why information-based complexity uses the real number model. Results in the real number model are essentially the same as in floating point arithmetic with fixed precision modulo two important assumptions, namely • we use only stable algorithms, • the approximation error is not too small, compared to the product of the condition number, the roundoff unit of floating point arithmetic, and the accumulation constant of a stable algorithm. We illustrate this by an example of solving nonlinear equations by bisection. We also indicate the possible tradeoffs between complexity and stability, and the need of using multiple or varying precision for ill-conditioned problems.