### A pseudo Laguerre method

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In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...

We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.