Winkler, Joab R.; Hasan, Madina; Lao, Xin Two methods for the calculation of the degree of an approximate greatest common divisor of two inexact polynomials. (English) Zbl 1261.12001 Calcolo 49, No. 4, 241-267 (2012). Summary: The calculation of the degree \(d\) of an approximate greatest common divisor of two inexact polynomials \(f(y)\) and \(g(y)\) reduces to the determination of the rank loss of a resultant matrix, the entries of which are functions of the coefficients of \(f(y)\) and \(g(y)\). This paper considers this issue by describing two methods to calculate \(d\), such that knowledge of the noise level imposed on the coefficients of \(f(y)\) and \(g(y)\) is not assumed. One method uses the residual of a linear algebraic equation whose coefficient matrix and right hand side vector are derived from the Sylvester resultant matrix \(S(f,g)\), and the other method uses the first principal angle between a line and a hyperplane, the equations of which are calculated from \(S(f,g)\). Computational results on inexact polynomials whose exact forms have multiple roots of high degree are shown and very good results are obtained. These results are compared with the rank loss of \(S(f,g)\) for the calculation of \(d\), and it is shown that this method yields incorrect results for these examples. Cited in 12 Documents MSC: 12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems) 12Y05 Computational aspects of field theory and polynomials (MSC2010) 65F99 Numerical linear algebra Keywords:greatest common divisor; polynomials; Sylvester resultant matrix Software:MultRoot PDFBibTeX XMLCite \textit{J. R. 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