Stability aspects in using parallel algorithms

After a detailed description of the theoretical foundations of forward error analysis formulated by Stummel, the problem of stability of parallel algorithms, which has as yet received very little attention in the literature, is discussed using arithmetic expressions as an example. The stability analysis includes several summation algorithms, the evaluation of products, parallelization of alternating expressions such as the Horner expression and finite continued fractions and finally general arithmetic expressions. For the CRAY-1 timing versus stability results are given for some of these expressions to classify their numerical quality.