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

Yuriy Volkov (2012)

Open Mathematics

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.

On algorithms for parabolic splines

Jiří Kobza (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On Best Cubature Formulas and Spline Interpolation.

M.E.A. El Tom (1979)

Numerische Mathematik

On optimal nodal splines and their applications.

Dagnino, C., Demichelis, V., Santi, Elisabetta (2003)

Rendiconti del Seminario Matematico

On smoothing conditions of multivariate splines.

Jerzy Stankiewicz (1997)

Collectanea Mathematica

On the control net of certain multivariate spline functions

Hans-Jörg Wenz (1994)

Acta Mathematica et Informatica Universitatis Ostraviensis

On the Convergence of Interpolating Periodic Spline Functions of High Degree.

M. von Golitschek (1972)

Numerische Mathematik

On the error estimation in numerical methods

V. A. Popov, A. S. Andreev (1984)

Banach Center Publications

On the numerical solution of an Abel integral equation

R. Smarzewski, H. Malinowski (1979)

Applicationes Mathematicae

On the smoothing spline regression models.

Breaz, Nicoleta, Aldea, Mihaela (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

On the two dimensional spline interpolation of Hermite-type.

Puşcaş, Mihaela (2003)

Acta Universitatis Apulensis. Mathematics - Informatics

Optimal discrete approximation of continuous linear operators applicable to control problems

Antonín Tuzar (1985)

Kybernetika

Optimal interpolatory splines using $B$ -spline representation

Jitka Machalová (2002)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Optimal quadratic interpolatory splines on general knotset

Jiří Kobza (2000)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Optimization of parameters in the Menzerath–Altmann law

Ján Andres, Lubomír Kubáček, Jitka Machalová, Michaela Tučková (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Four formulas of the Menzerath–Altmann law are tested from the point of view of their applicability and suitability. The accuracy of related approximations of measured data is examined by the least square method at first. Then the accuracy of calculated parameters in the formulas under consideration is compared statistically. The influence of neglecting parameter $c$ is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics....

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