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Title: On the Arithmetic of Errors
Authors: Markov, Svetoslav
Hayes, Nathan
Keywords: Computer Arithmetic
Error Analysis
Interval Arithmetic
Approximate Numbers
Algebra of Errors
Quasilinear Spaces
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 4, No 4, (2010), 447p-462p
Abstract: An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.
ISSN: 1312-6555
Appears in Collections:Volume 4 Number 4

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