Summary: A typical usage of computers in engineering is as follows: we are interested in some quantity \(y\) (e.g., the amount of oil in a given region), that is difficult or even impossible to measure directly. So we measure some physical quantities \(x_1, \dots,x_n\), that are connected with \(y\) (e.g., conductivity of different layers) and then compute \(y\) from the \(x_i\). Measurement errors in \(x_i\) lead to an error \(d\) in \(y\). The problem is to estimate \(d\), but methods of numerical analysis are often too difficult.
It is appropriate to consider the solution of this problem within the context of software engineering because we are essentially concerned with the quality of the results of our programs. We show that the solution of this problem is feasible, that is, it is possible to write a program that computes both \(y\) and its error estimate \(d\) from \(x_i\), given the measurements \(x_i\) and the range of possible measurement errors.
We show how this method can be parallelized and what parallelization model fits this problem best.