Notes on Error Estimates for Dot Product by Floating-Point Arithmetic

Abstract

Abstract. This paper is concerned with a rounding error analysis of dot product by floating-point arithmetic. Floating-point arithmetic is fast performed on recent architectures. However, since the number of total bits in floating-point format is finite, rounding errors may occur in arithmetic operations. Recently, new analysis of rounding errors for dot product was developed. We review the results of the error analysis of dot product and revise them.