Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis

Yuriy Volkov

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 352-356
  • ISSN: 2391-5455

Abstract

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We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.

How to cite

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Yuriy Volkov. "Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis." Open Mathematics 10.1 (2012): 352-356. <http://eudml.org/doc/269703>.

@article{YuriyVolkov2012,
abstract = {We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.},
author = {Yuriy Volkov},
journal = {Open Mathematics},
keywords = {Complete spline; Interpolation; B-splines; Banded system of equations; spline interpolation; Hermite boundary conditions; complete spline; B-spline representation; banded linear system},
language = {eng},
number = {1},
pages = {352-356},
title = {Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis},
url = {http://eudml.org/doc/269703},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Yuriy Volkov
TI - Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 352
EP - 356
AB - We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
LA - eng
KW - Complete spline; Interpolation; B-splines; Banded system of equations; spline interpolation; Hermite boundary conditions; complete spline; B-spline representation; banded linear system
UR - http://eudml.org/doc/269703
ER -

References

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  1. [1] Ahlberg J.H., Nilson E.N., Walsh J.L., The Theory of Splines and their Applications, Academic Press, New York-London, 1967 Zbl0158.15901
  2. [2] de Boor C., A Practical Guide to Splines, Appl. Math. Sci., 27, Springer, New York, 2001 Zbl0987.65015
  3. [3] Schumaker L.L., Spline Functions: Basic Theory, 3rd ed., Cambridge Math. Lib., Cambridge University Press, Cambridge, 2007 http://dx.doi.org/10.1017/CBO9780511618994 Zbl1123.41008
  4. [4] Volkov Yu.S., Totally positive matrices in the methods of constructing interpolation splines of odd degree, Siberian Adv. Math., 2005, 15(4), 96–125 
  5. [5] Zav’yalov Yu.S., Kvasov B.I., Miroshnichenko V.L., Methods of Spline-Functions, Nauka, Moscow, 1980 (in Russian) 

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