Czopik, J. The simultaneous determination of all zeros of a polynomial. (English) Zbl 0721.65023 Computing 45, No. 1, 79-91 (1990). A class of adaptive iterative methods of higher order for the simultaneous determination of all zeros of a polynomial is constructed. These methods preserve their order of convergence also in the case of multiple roots. Numerical examples are included. Reviewer: J.Czopik MSC: 65H05 Numerical computation of solutions to single equations 26C10 Real polynomials: location of zeros 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 12Y05 Computational aspects of field theory and polynomials (MSC2010) Keywords:adaptive iterative methods; zeros of a polynomial; order of convergence; multiple roots; Numerical examples PDFBibTeX XMLCite \textit{J. Czopik}, Computing 45, No. 1, 79--91 (1990; Zbl 0721.65023) Full Text: DOI References: [1] Alifanov O. M., Artiuchin E. A., Rumiancev S. V.: Extremal methods for the solution of ill-posed problems. Nauka. Moscow, 1988. In Russian. [2] Ben Israel, A.: A Newton-Raphson method for the solution of systems of equations. J. Math. Anal. Appl.15, 243–254 (1966). · Zbl 0139.10301 · doi:10.1016/0022-247X(66)90115-6 [3] Döring, B.: Über einige Klassen von Iterationsverfahren in Banach-Räumen. Math. Ann.187, 279–294 (1970). · Zbl 0237.65037 · doi:10.1007/BF01396457 [4] Ehrmann, H.: Konstruktion und Durchführung von Iterationsverfahren höherer Ordnung. Arch. Rat. Mech. Anat.4, 65–88 (1959/60). · Zbl 0089.32905 · doi:10.1007/BF00281379 [5] Gargantini, I., Henrici, P.: Circular arithmetic and the determination of polynomial zeros. Numer. Math.18, 305–320 (1972). · Zbl 0228.65038 · doi:10.1007/BF01404681 [6] Ioakimidis N. I., Anastasselou, E. G.: On the Simultaneous Determination of Zeros of Analytic or Sectionally Analytic Functions, Computing36, 239–247 (1987). · Zbl 0582.65035 · doi:10.1007/BF02240070 [7] Kerner, I.: Ein Gesamtschrittverfahren zur Berechnung der Nullstelle von Polynomen. Numer. Math.8, 290–294 (1966). · Zbl 0202.43605 · doi:10.1007/BF02162564 [8] Lawson, C. L., Hanson, R. J.: Solving least squares problems, Prentice-Hall, Englewood Cliffs, N.J., 1974. · Zbl 0860.65028 [9] Mostowski A., Stark M.: Higher algebra. Part II, Warsaw. 1974. In Polish. [10] Petković M. S., Stefanović L. U.: On a Second Order Method for the Simultaneous Inclusion of Polynomial Complex Zeros in Rectangular Arithmetic, Computing36, 249–261 (1986). · Zbl 0582.65036 · doi:10.1007/BF02240071 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.