Extension of floating-point filters to absolute and relative errors for numerical computation

Abstract

Abstract Although numerical computation is very fast, however, the results may not be accurate due to the accumulation of rounding errors. Consequently, much research has focussed on ways to verifying the accuracy of approximate solutions. Floating-point filters are one such technique. These can, for example, be used to guarantee the signs of computed results, such as those of the matrix determinants that are so important in the computational geometry field. In this paper, we extend floating-point filters to guarantee absolute and relative errors.