The Fundamental Theorems of Interval Analysis
M.H. van Emden, B. Moa
TL;DR
This paper clarifies the distinction between expressions and functions in interval arithmetic, providing precise definitions and proofs of the fundamental theorems to strengthen the theoretical foundation of interval analysis.
Contribution
It introduces a clear definition of the function computed by an expression and revises key theorems to improve rigor in interval analysis.
Findings
Defined the function computed by an expression in interval arithmetic
Re-stated and proved the fundamental theorems with improved rigor
Acknowledged contributions of P. Taylor
Abstract
Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis. Revision Feb. 10, 2009: added reference to and acknowledgement of P. Taylor.
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Taxonomy
TopicsNumerical Methods and Algorithms