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A reliable modification of the cross rule for rational Hermite interpolation (1992)

Beckermann, Bernhard ; Carstensen, Carsten

Springer

Numerical algorithms 3 (1992), S. 29-44

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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

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Interface problem in holonomic elastoplasticity (1993)

Carstensen, Carsten

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 16 (1993), S. 819-835

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: 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.

Additional Material: 1 Ill.