Simplication of symbolic-numerical interval expressions
Evgenija D. Popova, Ch. Ullrich · 1998
Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches | symbolic-algebraic and interval-arithmetic | are used separately.Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the \size" of the end-points.In this paper we propose a methodology for \true" symbolic-algebraic manipulations on symbolic-numerical 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 simpli cation of symbolicnumerical expressions involving intervals is given and some of the wider implications of the theory pertaining to interval algebraic problems are discussed.