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

Henryk Woźniakowski
1999 Theoretical Computer Science  
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 l we use only stable algorithms, l 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
more » ... near 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. First of all, we stress that the real number model is used in many areas of computations. It is almost universally used in scientific computing and numerical analysis. This model has been used in algebraic complexity already in the 1950s in the work of *
doi:10.1016/s0304-3975(98)00300-4 fatcat:bypyiuafj5cwriyzg2c3rl6jba