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  • 1
    Electronic Resource
    Electronic Resource
    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
    Keywords: 65H05 ; 65H10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388681
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    Paper (German National Licenses)
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  • 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
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    Paper (German National Licenses)
    Fulltext
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