A pseudo Laguerre method
Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach.
Chromatic roots of a ring of four cliques.
Enclosing roots of polynomial equations and their applications to iterative processes.
FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials
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...
Fractional double Newton step properties for polynomials with all real zeros
Integral minimalisations improvement for Murphy's polynomial selection algorithm.
On the local convergence of Kung-Traub's two-point method and its dynamics
In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test...
Simultaneous triangularization of commuting matrices for the solution of polynomial equations
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.