Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials (1993)
    Springer
    BIT 33 (1993), S. 63-73 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65H05 ; CR: 5.15 ; polynomial zeros ; Durand-Kerner method ; simultaneous root finding method ; factorization of polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Durand-Kerner's method for simultaneous rootfinding of a polynomial is locally second order convergent if all the zeros are simple. If this condition is violated numerical experiences still show linear convergence. For this case of multiple roots, Fraigniaud [4] proves that the means of clustering approximants for a multiple root is a better approximant for the zero and called this Quadratic-Like-Convergence of the Means. This note gives a new proof and a refinement of this property. The proof is based on the related Grau's method for simultaneous factoring of a polynomial. A similar property of some coefficients of the third order method due to Börsch-Supan, Maehly, Ehrlich, Aberth and others is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990344
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    A reliable modification of the cross rule for rational Hermite interpolation (1992)
    Springer
    Numerical algorithms 3 (1992), S. 29-44 
    Details
    ISSN: 1572-9265
    Keywords: AMS(MOS) 65D05 ; 30E05 ; CR G1.2 ; Rational interpolation ; Newton-Padé approximation ; cross rule ; reliability ; singular rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Claessens' cross rule [8] enables simple computation of the values of the rational interpolation table if the table is normal, i.e. if the denominators in the cross rule are non-zero. In the exceptional case of a vanishing denominator a singular block is detected having certain structural properties so that some values are known without further computations. Nevertheless there remain entries which cannot be determined using only the cross rule. In this note we introduce a simple recursive algorithm for computation of the values of neighbours of the singular block. This allows to compute entries in the rational interpolation table along antidiagonals even in the presence of singular blocks. Moreover, in the case of non-square singular blocks, we discuss a facility to monitor the stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02141913
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...