Reducibility Among Floating-Point Graphs
Donald B. Johnson, Webb Miller, Brian Minnihan, Celia Wrathall · Journal of the ACM · 1979
The graph-theoretical models of this paper can be used to compare the rounding error behavior of numerical programs The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors at each arithmetic operation Models constructed on th~s assumpuon are more tractable than would be the case under more realistic assumptions There are identified two easily tested condmons on programs which guarantee that" error analyses are relatively lnsensmve to the particular graph model employed The development has the addmonal benefit of sometimes providing an elementary proof that one program is comparable in stablhty to another Examples of such results are gwen KEY WORDS AND PHRASES rounding errors, numerical stability, arithmetic graphs CR CATEGORIES 5 11, 5 14In order to represent programs as "arithmetic graphs," we restrict attention to straight-