Sharpness in interval computations
If \(f(x)\) is an arithmetic expression for the multivariate rational function \(f\), the interval extension \(f(X)\) arises from \(f(x)\) by replacing the variable \(x\) by the interval or interval variable \(X\). In general, \(f(X)\) is a proper superset of the range of \(f\) over \(X\). -- The author pursues an interesting concept to determine whether \(f(X)\) is equal to the range or whether one of the endpoints of \(f(X)\) coincides with an endpoint of the range. This concept is based on a so-called endpoint arithmetic, where the dependency of the endpoints of \(f(X)\) on the endpoints of \(X\) is investigated.
scientific article; zbMATH DE number 1045479