A multivariate rational interpolation with no poles in ℝ^{m}
Year 2015,
Volume: 3 Issue: 1, 19 - 28, 22.12.2014
Osman Işık
Zekeriya Güney
Mehmwt Sezer
Abstract
The aim of this paper is to construct a family of rational interpolants that have no poles inRm. This method is an extensionof Floater and Hormanns method [1]. A priori error estimate for the method is given under some regularity conditions
References
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- J. P. Berrut, H. D. Mittelmann, Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Appl., 33 (1997) 77-86.
- J. P. Berrut, Rational functions for guaranteed and experimentally well-conditioned global interpolation, Comput. Math. Appl., 15 (1988) 1-16.
- J. P. Berrut, Barycentric Lagrange interpolation, SIAM Rev., 46 (2004) 501-517.
- J. P. Berrut, R. Baltensperger, H. D. Mittelmann, Recent developments in barycentric rational interpolation. Trends and Applications in Constructive Approximation(M. G. de Bruin, D. H. Mache, and J. Szabados, eds.), International Series of Numerical Mathematics, 151 (2005) 27-51.
- A. Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer, New York, 2007.
- G. M. Phillips, Interpolation and Approximation by Polynomials,Springer, New York, 2003.
- B. M¨oßner, U. Reif, Error bounds for polynomial tensor product interpolation, Computing, 86 (2009) 185-197.
- A. Sommariva, M. Vianello, R. Zanovello, Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005) 79-94.
A multivariate rational interpolation with no poles in
Year 2015,
Volume: 3 Issue: 1, 19 - 28, 22.12.2014
Osman Işık
Zekeriya Güney
Mehmwt Sezer
References
- M.S. Floater, K. Hormann, Barycentric rational interpolation with no poles and high rates of approximation, Numerische Mathematik, 107 (2006) 315-331.
- J. P. Berrut, H. D. Mittelmann, Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Appl., 33 (1997) 77-86.
- J. P. Berrut, Rational functions for guaranteed and experimentally well-conditioned global interpolation, Comput. Math. Appl., 15 (1988) 1-16.
- J. P. Berrut, Barycentric Lagrange interpolation, SIAM Rev., 46 (2004) 501-517.
- J. P. Berrut, R. Baltensperger, H. D. Mittelmann, Recent developments in barycentric rational interpolation. Trends and Applications in Constructive Approximation(M. G. de Bruin, D. H. Mache, and J. Szabados, eds.), International Series of Numerical Mathematics, 151 (2005) 27-51.
- A. Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer, New York, 2007.
- G. M. Phillips, Interpolation and Approximation by Polynomials,Springer, New York, 2003.
- B. M¨oßner, U. Reif, Error bounds for polynomial tensor product interpolation, Computing, 86 (2009) 185-197.
- A. Sommariva, M. Vianello, R. Zanovello, Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005) 79-94.