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

Open Mathematics (2012)

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

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topYuriy 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

top- [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] de Boor C., A Practical Guide to Splines, Appl. Math. Sci., 27, Springer, New York, 2001 Zbl0987.65015
- [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] 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] Zav’yalov Yu.S., Kvasov B.I., Miroshnichenko V.L., Methods of Spline-Functions, Nauka, Moscow, 1980 (in Russian)

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