An algebraic model for the propagation of errors in matrix calculus

Abstract

We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) additive group. The algebraic properties of external numbers formalize common error analysis, with rules for calculation which are a sort of mellowed form of the axioms for real numbers.

Keywords

• matrix calculus
• error propagation
• rank
• external numbers
• 03h05
• 15a03
• 15a09
• 15b33
• 65f99