Feinstein, Jaime The negative Routh test and its application to the cases of vanishing leading elements and imaginary roots. (English) Zbl 0615.65051 IEEE Trans. Autom. Control 30, 164-165 (1985). The ordinary Routh test furnishes in a straightforward manner the number \(r_+\), of positive roots of a polynomial of degree n. A modification that allows one to obtain the number \(r_-\) of negative roots in the same way is presented. Thus, the number \(r_ 0\) of (purely) imaginary roots is immediately found as \(n-(r_++r_-)\). The modified test is especially useful when there is a first column vanishing element. Cited in 2 Documents MSC: 65H05 Numerical computation of solutions to single equations 12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems) 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) Keywords:location of zeros; negative Routh test; positive roots of a polynomial PDFBibTeX XMLCite \textit{J. Feinstein}, IEEE Trans. Autom. Control 30, 164--165 (1985; Zbl 0615.65051) Full Text: DOI