Interval control methods of rounding error in numerical calculation

The analysis of the errors arising in numerical calculation can contribute to identify the reliability of calculated results, avoid error hazards and improve the accuracy of calculations. It is one of the research focuses of numerical calculation to efficiently control the errors by improved algorithms. In the actual process of calculations, the number of significant digits always only gets limited because of the length restrictions of the numbers in the computer. Therefore, these methods for some algorithms, especially when the problems are ill-conditioned or unstable, may not be able to get the desired results, that is, the errors can't effectively be controlled. The use of interval calculation methods is able to more effectively solve these problems. Furthermore, some mathematical softwares, such as mathematica, provided the infinite-precision calculation methods by which we can get real results for the specific numeric type.