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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

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: 1, 19 - 28, 22.12.2014

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

Journal Section Articles
Authors

Osman Işık This is me

Zekeriya Güney This is me

Mehmwt Sezer This is me

Publication Date December 22, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Işık, O., Güney, Z., & Sezer, M. (2014). A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences, 3(1), 19-28.
AMA Işık O, Güney Z, Sezer M. A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences. December 2014;3(1):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. 1 (December 2014): 19-28.
EndNote Işık O, Güney Z, Sezer M (December 1, 2014) A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences 3 1 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. 1, pp. 19–28, 2014.
ISNAD Işık, Osman et al. “A Multivariate Rational Interpolation With No Poles in ℝ^{m}”. New Trends in Mathematical Sciences 3/1 (December 2014), 19-28.
JAMA Işık O, Güney Z, Sezer M. A multivariate rational interpolation with no poles in ℝ^{m}. New Trends in Mathematical Sciences. 2014;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. 1, 2014, 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. 2014;3(1):19-28.