Linear Rational Interpolant

Dr. (Mrs) Mridula Chaturvedi

doi:https://doi.org/10.14445/22315373/IJMTT-V60P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 3 | Year 2018 | Article Id. IJMTT-V60P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P526

Linear Rational Interpolant

Dr. (Mrs) Mridula Chaturvedi

Abstract

An explicit representation of a C0 piecewise rational function is developed which can be used to solve the problems of shape preserving interpolation. It is shown that the interpolation method can be applied to convex and/or monotonic set of data.

Keywords

Rational, Shape Preserving, Monotonic, Convex Interpolation.

References

[1] R.Delbourgo, Shape preserving interpolation to convex, data by rational functions with quadratic numerator and linear denominator; IMA Journal of Numer. Anal., 9 (1989), 123-136.
[2] R.Delbourgo and J. A. Gregory, C2-rational quadratic interpolation to monotonic data; IMA Journal of Numer. Anal., 3 (1983), 141-152.
[3] R.Delbourgo and J. A. Gregory, Shape preserving piecewise rational interpolation; SIAM J. Sci. stat. comput. 6 (1985), 967-976.
[4] F.N.Fritsch and R. E. Carlson, Monotone piecewise cubic interpolants; SIAM J. Numer Anal; 17 (1980), 238-246.
[5] F.N.Fritsch and J. Butland, A method for constructing local monotone piecewise cubic interpolants; SIAM J. Sci. stat. Comput; 5 (1984), 300-304.
[6] J. A.Gregory and R. Delbourgo, Piecewise rational quadratic interpolation to monotonic data; IMA Journal of Numer. Anal., 2 (1982), 123-130.
[7] M.K.Ismail, Monotonicity preserving interpolation using C2-rational cubic Bezier Curves in mathematical methods in CAGD II; (Ed. T. Lyche and L. L. Schumaker). Academic Press, New York (1982) 343-350.
[8] D.F.Mc Allister, E. Passow and J. A. Roulier, Algorithm for computing shape preserving spline interpolations to data; Math. comp, 31 (1971), 717-725.
[9] D.F.Mc Allister, and J. A. Roulier, Interpolation by convex quadratic splines; Math. Comput., 32 (1978), 1154-1162.
[10] E.Passow and J. A. Roulier, Monotone and convex spline interpolation; SIAM J. Numer Anal; 14 (1977), 904-909.

Citation :

Dr. (Mrs) Mridula Chaturvedi, "Linear Rational Interpolant," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 3, pp. 168-172, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P526