Root squaring using level-index arithmetic
The symmetric level-index (SLI) system is a system for representing numbers, which eases the monitoring of precision while avoiding the problem associated with overflow and underflow. In SLI system any real number X is represented by its mapping in computer x, a sign s(X) and a reciprocation indicator r(X), so that we have \(X=s(X)\phi (x)^{r(X)},\) where the generalized exponential function \(\phi\) is defined by \(\phi (x)=x,\quad x\in [0,1),\) and \(\phi (x)=e^{\phi (x-1)},\quad x\geq 1.\) The authors discuss the essentials of SLI and apply it to Graeffe's root squaring method for finding zeros of polynomials. Numerical results from test examples are given.
scientific article; zbMATH DE number 4128303
scientific article