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
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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
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.
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.