Computation of rational interpolants with prescribed poles

DOI10.1016/0377-0427(89)90302-6zbMath0682.65001OpenAlexW2064898684MaRDI QIDQ1824339

Mariano Gasca, José-Javier Martıńez, Günter W. Mühlbach

Publication date: 1989

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(89)90302-6

zbMATH Keywords

algorithmrational interpolationprescribed polesHermite dataCauchy- Vandermonde determinant

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Numerical interpolation (65D05)

Related Items (19)

Factorizations of confluent Cauchy-Vandermonde matrices ⋮ On multivariate interpolation by generalized polynomials on subsets of grids ⋮ On rational B-splines with prescribed poles ⋮ On Hermite interpolation by Cauchy-Vandermonde systems: The Lagrange formula, the adjoint and the inverse of a Cauchy-Vandermonde matrix ⋮ The barycentric weights of rational interpolation with prescribed poles ⋮ The work of Mariano Gasca ⋮ Factorizations of Cauchy-Vandermonde matrices ⋮ Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems ⋮ Accurate computations for eigenvalues of products of Cauchy-polynomial-Vandermonde matrices ⋮ Lax integrability and the peakon problem for the modified Camassa-Holm equation ⋮ The Neville-Aitken formula for rational interpolants with prescribed poles ⋮ Accurate computations of eigenvalues of quasi-Cauchy-Vandermonde matrices ⋮ Displacement structure approach to Cauchy and Cauchy-Vandermonde matrices: Inversion formulas and fast algorithms ⋮ Generalized confluent Cauchy-Vandermonde matrices: Displacement structures, inversion formulas and tangential interpolations ⋮ On interpolation by rational functions with prescribed poles with applications to multivariate interpolation ⋮ On the solvability of bivariate Hermite-Birkhoff interpolation problems ⋮ Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights. I ⋮ Interpolation by Cauchy-Vandermonde systems and applications ⋮ A note on the Hermite interpolation

Cites Work

• A generalization of Sylvester's identity on determinants and some applications
• Linear extrapolation by rational functions, exponentials and logarithmic functions
• On Lagrange and Hermite interpolation in \(R^ k\).
• The mühlbach-neville-aitken algorithm and some extensions
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