Algorithm 882

Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods. We present a numerical procedure to compute the nodes and weights in rational Gauss-Chebyshev quadrature formulas. Under certain conditions on the poles, these nodes are near best for rational interpolation with prescribed poles (in the same sense that Chebyshev points are near best for polynomial interpolation). As an illustration, we use these interpolation points to solve a differential equation with an interior boundary layer using a rational spectral method. The algorithm to compute the interpolation points (and, if required, the quadrature weights) is implemented as a Matlab program.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 10 articles )

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  1. Deckers, Karl; Mougaida, Ahlem; Belhadjsalah, Hédi: Algorithm 973: Extended rational Fejér quadrature rules based on Chebyshev orthogonal rational functions (2017)
  2. Corless, Robert M.; Fillion, Nicolas: A graduate introduction to numerical methods. From the viewpoint of backward error analysis (2013)
  3. Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar: Polynomial algebra for Birkhoff interpolants (2011)
  4. Deckers, K.; Bultheel, A.; Van Deun, J.: A generalized eigenvalue problem for quasi-orthogonal rational functions (2011)
  5. Druskin, Vladimir; Knizhnerman, Leonid; Simoncini, Valeria: Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation (2011)
  6. Knizhnerman, L.; Simoncini, V.: Convergence analysis of the extended Krylov subspace method for the Lyapunov equation (2011)
  7. Chesnokov, Andrey; Deckers, Karl; Van Barel, Marc: A numerical solution of the constrained weighted energy problem (2010)
  8. Van Deun, Joris: Computing near-best fixed pole rational interpolants (2010)
  9. Bultheel, Adhemar; Cruz-Barroso, Ruymán; Deckers, Karl; González-Vera, Pablo: Rational Szegő quadratures associated with Chebyshev weight functions (2009)
  10. Van Deun, Joris; Deckers, Karl; Bultheel, Adhemar; Weideman, J. A. C.: Algorithm 882: Near-best fixed pole rational interpolation with applications in spectral methods. (2008) ioport