Error-Free Transformations in Real and Complex Floating Point Arithmetic
Stef Graillat, Valérie Ménissier-Morain, Département Calcul Scientifique · 2007
Abstract — Error-free transformation is a concept that makes it possible to compute accurate results within a floating point arithmetic. Up to now, it has only be studied for real floating point arithmetic. In this short note, we recall the known error-free transformations for real arithmetic and we propose some new error-free transformations for complex floating point arithmetic. This will make it possible to design some new accurate algorithms for summation, dot product and polynomial evaluation with complex entries. 1.