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A multivariate rational interpolation with no poles in ℝ^{m}

Year 2015, Volume: 3 Issue: 3, 19 - 28, 26.06.2015

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

Keywords

Rational interpolant Floater and Hormanns method Error estimate

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.

A multivariate rational interpolation with no poles in

Year 2015, Volume: 3 Issue: 3, 19 - 28, 26.06.2015

Osman Işık Zekeriya Güney Mehmwt Sezer

Abstract

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.
There are 9 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Osman Işık

Zekeriya Güney

Mehmwt Sezer

Publication Date June 26, 2015
Published in Issue Year 2015 Volume: 3 Issue: 3

Cite

APA Işık, O., Güney, Z., & Sezer, M. (2015). A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences, 3(3), 19-28.
AMA Işık O, Güney Z, Sezer M. A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences. June 2015;3(3):19-28.
Chicago Işık, Osman, Zekeriya Güney, and Mehmwt Sezer. “A Multivariate Rational Interpolation With No Poles in ℝ^{m}”. New Trends in Mathematical Sciences 3, no. 3 (June 2015): 19-28.
EndNote Işık O, Güney Z, Sezer M (June 1, 2015) A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences 3 3 19–28.
IEEE O. Işık, Z. Güney, and M. Sezer, “A multivariate rational interpolation with no poles in ℝ^{m}”, New Trends in Mathematical Sciences, vol. 3, no. 3, pp. 19–28, 2015.
ISNAD Işık, Osman et al. “A Multivariate Rational Interpolation With No Poles in ℝ^{m}”. New Trends in Mathematical Sciences 3/3 (June 2015), 19-28.
JAMA Işık O, Güney Z, Sezer M. A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences. 2015;3:19–28.
MLA Işık, Osman et al. “A Multivariate Rational Interpolation With No Poles in ℝ^{m}”. New Trends in Mathematical Sciences, vol. 3, no. 3, 2015, pp. 19-28.
Vancouver Işık O, Güney Z, Sezer M. A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences. 2015;3(3):19-28.