Construction of a Family of \(C^1\) Convex Integro Cubic Splines

Authors

  • Zhanlav Tugal Institute of Mathematics and Digital Technologies, Mongolian Academy of Sciences, Ulaanbaatar
  • Mijiddorj Renchin-Ochir Department of Informatics, Mongolian National University of Education, Ulaanbaatar

DOI:

https://doi.org/10.26713/cma.v11i4.1386

Keywords:

Shape-preserving, Approximation, Integro spline

Abstract

We construct a family of monotone and convex \(C^1\) integro cubic splines under a strictly convex position of the dataset. Then, we find an optimal spline by considering its approximation properties. Finally, we give some examples to illustrate the convex-preserving properties of these splines.

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References

H. Akima, A new method of interpolation and smooth curve fitting based on local procedures, Journal of Association for Computing Machinery 17 (1970), 589 – 602, DOI: 10.1145/321607.321609.

H. Behforooz, Approximation by integro cubic splines, Applied Mathematics and Computation 175 (2006), 8 – 15, DOI: 10.1016/j.amc.2005.07.066.

M. Fischer and P. Oja, Monotonicity preserving rational spline histopolation, Journal of Computational and Applied Mathematics 175 (2005), 195 – 208, DOI: 10.1016/j.cam.2004.05.009.

M. Fischer, P. Oja and H. Trossmann, Comonotone shape-preserving spline histopolation, Journal of Computational and Applied Mathematics 200 (2007), 127 – 139, DOI: 10.1016/j.cam.2005.12.010.

M. Kaykobad, Positive solutions of positive linear systems, Linear Algebra and its Applications 64 (1985), 133 – 140, DOI: 10.1016/0024-3795(85)90271-X.

T.-W. Kim and B. Kvasov, A shape-preserving approximation by weighted cubic splines, Journal of Computational and Applied Mathematics 236 (2012), 4383 – 4397, DOI: 10.1016/j.cam.2012.04.001.

B. Mulansky and J. W. Schmidt, Convex interval interpolation using a three-term staircase algorithm, Numerische Mathematik 82 (1999), 313 – 337, DOI: 10.1007/s002110050421.

E. Neuman, Uniform approximation by some Hermite interpolating splines, Journal of Computational and Applied Mathematics 4 (1978), 7 – 9, https://core.ac.uk/download/pdf/81978018.pdf.

J. W. Schmidt and W. HeíŸ, Shape preserving (C^2)-spline histopolation, Journal of Approximation Theory 75 (1993), 325 – 345, DOI: 10.1006/jath.1993.1106.

J. W. Schmidt and W. HeíŸ, An allways successful method in univariate convex (C^2)-interpolation, Numerische Mathematik 71 (1995), 237 – 252, DOI: 10.1007/s002110050143.

J. W. Schmidt, Staircase algorithm and construction of convex spline interpolats up to the continuity (C^3), Computers & Mathematics with Applications 31 (1996), 67 – 79, DOI: 10.1016/0898-1221(95)00218-9.

T. Zhanlav, Shape preserving properties of (C^1) cubic spline approximations, Scientific Transaction NUM 7 (2000), 14 – 20, URL https://www.researchgate.net/profile/T_Zhanlav/publication/307632050_Shape_preserving_properties_of_C1_cubic_spline_approximations/links/5f555a5a458515e96d35c24f/Shape-preserving-properties-of-C1-cubic-spline-approximations.pdf.

T. Zhanlav, Shape preserving properties of some (C^2) cubic spline approximations,Scientific Transaction NUM 7 (2000), 21 – 35, URL https://www.researchgate.net/profile/T_Zhanlav/publication/307631606_Shape_preserving_properties_of_some_C2_cubic_spline_approximations/links/5f555c4c92851c250b995dc1/Shape-preserving-properties-of-some-C2-cubic-spline-approximations.pdf.

T. Zhanlav and R. Mijiddorj, Convexity and monotonicity properties of the local integro cubic spline, Applied Mathematics and Computation 293 (2017), 131–137, DOI: 10.1016/j.amc.2016.08.017.

P. Žencák, The convex interpolation of histogram by polynomial splines: The existence theorem, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 41 (2002), 175–182, URL: https://dml.cz/bitstream/handle/10338.dmlcz/120449/ActaOlom_41-2002-1_16.pdf.

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Published

31-12-2020
CITATION

How to Cite

Tugal, Z., & Renchin-Ochir, M. (2020). Construction of a Family of \(C^1\) Convex Integro Cubic Splines. Communications in Mathematics and Applications, 11(4), 527–538. https://doi.org/10.26713/cma.v11i4.1386

Issue

Vol. 11 No. 4 (2020)

Section

Research Article

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