Numerical calculations accuracy issues in basic programming teaching

Abstract

[...] In the chapter there are discussed basic types of floating-point calculations errors which results from the application of numerical methods: • errors resulting from number systems differences (binary vs. decimal), • errors resulting from differences how the input data is treated (discrete vs. continuous), • errors resulting from limitations of binary arithmetic. There are also served short characteristics of the errors, in many cases supplemented by examples of their occurrence. The authors pointed out, that the standard level of accuracy offered by widely applied developments environments are not sufficient to achieve the highest precision in case of today's computational problems. Some methods to achieve this goal are given. There are discussed the effects of propagation and accumulation of basic types of computational errors aroused as an effect of arithmetic operations and selected functions transformations.