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Simplification of SymbolicNumerical Interval Expressions
 in Gloor, O. (Ed.): Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, ACM
, 1998
"... Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches  symbolicalgebraic and intervalarithmetic  are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the "si ..."
Abstract

Cited by 5 (2 self)
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Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches  symbolicalgebraic and intervalarithmetic  are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the "size" of the endpoints. In this paper we propose a methodology for "true" symbolicalgebraic manipulations on symbolicnumerical interval expressions involving interval variables instead of symbolic intervals. Due to the better algebraic properties, resembling to classical analysis, and the containment of classical interval arithmetic as a special case, we consider the algebraic extension of conventional interval arithmetic as an appropriate environment for solving interval algebraic problems. Based on the distributivity relations, a general framework for simplification of symbolicnumerical expressions involving intervals is given and some of the wider implications of the theory pertaining to inte...
Directed Interval Arithmetic in Mathematica: Implementation and Applications
, 1996
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Abstract Simplification of SymbolicNumerical Interval Expressions ∗
"... Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches — symbolicalgebraic and intervalarithmetic — are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the “size ” of t ..."
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Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches — symbolicalgebraic and intervalarithmetic — are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the “size ” of the endpoints. In this paper we propose a methodology for “true ” symbolicalgebraic manipulations on symbolicnumerical interval expressions involving interval variables instead of symbolic intervals. Due to the better algebraic properties, resembling to classical analysis, and the containment of classical interval arithmetic as a special case, we consider the algebraic extension of conventional interval arithmetic as an appropriate environment for solving interval algebraic problems. Based on the distributivity relations, a general framework for simplification of symbolicnumerical expressions involving intervals is given and some of the wider implications of the theory pertaining to interval algebraic problems are discussed. 1