Minimization of rounding errors algebraically by use of coding theory

Abstract

In this paper we consider the floating-point sum of positive terms. Among the algebraically equivalent schemes we determine the ones which lead to the minimum of the upper bound of the rounding errors. We also provide lower and upper bounds for this minimum by relating this problem to the coding theory.

Keywords:

• Rounding error
• binary trees
• Huffman's algorithm
• H-trees

C.R. Categories::

• CR: G.1.O
• AMS(M0S): 65605