This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
5. References
O. ABERTH: Iteration methods for finding all zeros of a polynomial simultaneously. Math.Comp. 27, 339–344 (1973)
G.ALEFELD, J.HERZBERGER: Einführung in die Intervallrechnung B.I.Wissenschaftsverlag, Mannheim, 1974
G. ALEFELD, J. HERZBERGER: On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots, SIAM J.Numer.Anal. 11, 237–243 (1974)
W. BÖRSCH-SUPAN: A posteriori error bounds for the zeros of polynomials, Numer.Math. 5, 380–398 (1963)
W. BÖRSCH-SUPAN: Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation, Numer.Math. 14, 287–296 (1970)
D. BRAESS, K.P. HADELER: Simultaneous inclusion of the zeros of a polynomial, Numer.Math. 21, 161–165 (1973)
D. BRAESS, H. SPÄTH: Maßnahmen zur globalen Konvergenzerzwingung beim Newton'schen Verfahren für spezielle nichtlineare Gleichungssysteme, ZAMM 47, 409–410 (1967)
P. BYRNEV, K. DOCHEV: Certain modifications of Newton's method for the approximate solution of algebraic equations, Zh.Vych.Mat. 4, 915–920 (1964)
K. DOCHEV, L. ILLIEF: Über Newton'sche Iterationen, Wiss.Z.TH Dresden 12, 117–118 (1963)
E. DURAND: Solution numérique des équations algébraique (tome 1), Masson, Paris, 1960
L.W. EHRLICH: A modified Newton method for polynomials, Comm.ACM 10, 107–108 (1967)
L. ELSNER: A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem, Numer.Math. 21, 425–427 (1973)
I. GARGANTINI, P. HENRICI: Circular arithmetic and the determination of polynomial zeros, Numer.Math. 18, 305–320 (1972)
M. GUTKNECHT: A posteriori error bounds for the zeros of a polynomial, Numer.Math. 20, 139–148 (1972)
P. HENRICI: Applied and computational complex analysis, John Wiley, New York, 1974
A.S. HOUSEHOLDER: The numerical treatment of a single nonlinear equation, McGraw-Hill, New York, 1970
A.S. HOUSEHOLDER: The theory of matrices in numerical analysis, Blaisdell, New York, 1964
I.O. KERNER: Ein Gesamtschrittverfahren zur Berechnung von Nullstellen von Polynomen, Numer.Math. 8, 290–294 (1966)
I.O.KERNER: Simultaneous displacement of polynomial roots if real and simple, Comm.ACM, 273, (1966)
M.MARDEN: Geometry of polynomials, AMS Math.Surveys 3, 1966
L.M. MILNE-THOMPSON: The calculus of finite differences, Macmillan, London, 1933
J.W. SCHMIDT: Eine Anwendung des Brouwer'schen Fixpunktsatzes zur Gewinnung von Fehlerschranken für Näherungen von Polynomnullstellen, Beiträge zur Numerischen Mathematik 6, 158–163, (1977)
J.W. SCHMIDT, H. DRESSEL: Fehlerabschätzungen bei Polynomgleichungen mit dem Fixpunktsatz von Brouwer, Numer.Math. 10, 42–50 (1967)
B.T. SMITH: Error bounds for the zeros of a polynomial based upon Gershgorin's theorems, J.Assoc.Comput.Mach. 17, 661–674 (1970)
K.WEIERSTRASS: Neuer Beweis des Satzes, dass jede ganze rationale Funktion einer Veränderlichen dargestellt werden kann als Product aus linearen Funktionen derselben Veränderlichen, Ges.Werke 3, 251–269
W.WERNER: A generalized Frobenius normal form and some applications, submitted for publication
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Werner, W. (1982). On the simultaneous determination of polynomial roots. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069383
Download citation
DOI: https://doi.org/10.1007/BFb0069383
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11602-8
Online ISBN: 978-3-540-39379-5
eBook Packages: Springer Book Archive
