Some remarks on Rational Barycentric Interpolation
Keywords:
Polynomial interpolation, rational interpolation, barycentric interpolationAbstract
Linear barycentric rational interpolant are a specific type of rational interpolants, defined by weight independent of function. These interpolants have recently been a valuable alternative to more classical methods of interpolation. Rational interpolation gives a much better approximation than polynomial, but it is difficult to avoid poles and unattainable points.
In this paper , discuss the use of rational interpolation development, then we try to introduce another barycentric rational interpolant that provides a good result.
References
Abumaryam, S. The Convergence of Polynomial Interpolation and Runge Phenomenon. Sirte University Scientific Journal (Applied Sciences), 2018.
Berrut,J. And Mittelmann ,H. Lebesgue Constant Minimizing Linear Rational Interpolation of Continuous Function over the Interval .,Journal of Computational and Applied Mathematics, 1997.
Berrut,J. And Mittelmann ,H. Matrices for the Direct Determination of the Barycentric Weights of Rational Interpolation.,Journal of Computational and Applied Mathematics, 1997.
Berrut, J. And Mittelmann,H. Rational interpolation through the optimal attachment of poles to the interpolating polynomial., Journal of Numerical Algorithms, 2000.
Berrut, J, P. Rational Functions for Guaranteed and Experimentally Well Conditioned Global Interpolation. , Computer Math Applic, 1988.
Berrut, J, P. And Trefethen, L, N, Barycentric Lagrange Interpolation. , SIAM Review, 2004.
Berrut, J, P. Baltensperger, R. And Mittelmann, Hans , D. Recent Development in Barycentric Rational Inter-polation. , International Series of Numerical Mathematics, 2005.
Bos, L. De Marchi, S. Hormann, K. And Sildon, J,Bounding the Lebesgue Constant of Berrut's Rational Interpolant at Equidistant Nodes . , Journal of Computational and Applied Mathematics, 2013.
Davis, P,Interpolation and Approximation . ,Blaisdell Publishing Company,1965.
Floater, M. And Hormann ,k. Barycentric Rational Interpolation with no Poles and High Rates of Approximation., Numerical Math, 2007.
Henrici, P. Elements of Numerical Analysis. , Wiley,New York, 1964.
Higham N, J, The numerical stability of Barycentric Lagrange interpolation . , IMA Journal of Numerical Analysis, 2004.
Hormann, K. Bos, L. And De Marchi,S,On the Lebesgue Constant of Berrut's Rational Interpolant at General Nodes . , Journal of Computational and Applied Mathematics, 2011.
Polezzi, M. And Ranga, A.On the denominator values and barycentric weights of rational interpolants., Journal of Computational and Applied Mathematics, 2007.
Powell, M,Approximation Theory and Methods. , Cambridge University, 2004.
Schneider, C. And, Werner, W. Some New Aspects of Rational Interpolation. , Mathematics of Computation,1986.
Trefethen, N,Approximation Theory and Approximation Practice. , University of Oxford, 2012.
Webb, M and Trefethen, N and Gonnet, P.Stability of barycentric interpolation formulas for extrapolation.,SIAM J. Sci. Comput, 2012.
Werner, w,Polynomial Interpolation: Lagrange versus Newton. , Mathematics of Computation, 1984.
Winrich, L. B.Note on a comparison of evaluation schemes for the Interpolation Polynomials. , Computer Journal, 1969.
Zhang, R,An Improved Upper Bound on the Lebesgue Constant of Berrut's Rational Interpolation Operator . ,Journal of Computational and Applied Mathematics, 2014.
Zhu,X. And Gonqqin ,H.A method for directly _nding the denominator values of rational interpolants.,Journal of Computational and Applied Mathematics, 2002.
