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  • Artikel: DFG Deutsche Nationallizenzen  (4)
  • 1990-1994  (4)
  • 1
    Digitale Medien
    Digitale Medien
    On a class of higher order methods for simultaneous rootfinding of generalized polynomials (1993)
    Springer
    Numerische Mathematik 64 (1993), S. 69-84 
    Details
    ISSN: 0945-3245
    Schlagwort(e): 65H05 ; 65H10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Using the argument principle higher order methods for simultaneous computation of all zeros of generalized polynomials (like algebraic, trigonometric and exponential polynomials or exponential sums) are derived. The methods can also be derived following the continuation principle from [3]. Thereby, the unified approach of [7] is enlarged to arbitrary orderN. The local convergence as well as a-priori and a-posteriori error estimates for these methods are treated on a general level. Numerical examples are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01388681
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65H05 ; CR: 5.15 ; polynomial zeros ; Durand-Kerner method ; simultaneous root finding method ; factorization of polynomials
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01990344
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    A reliable modification of the cross rule for rational Hermite interpolation (1992)
    Springer
    Numerical algorithms 3 (1992), S. 29-44 
    Details
    ISSN: 1572-9265
    Schlagwort(e): AMS(MOS) 65D05 ; 30E05 ; CR G1.2 ; Rational interpolation ; Newton-Padé approximation ; cross rule ; reliability ; singular rules
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02141913
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Interface problem in holonomic elastoplasticity (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 819-835 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure.The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670161105
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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