A variational approach to spline functions theory.
Micula, G. (2003)
Rendiconti del Seminario Matematico
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Micula, G. (2003)
Rendiconti del Seminario Matematico
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Branga, Adrian (1996)
General Mathematics
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Pílnikova, Jana, Chalmovianský, Pavel (1999)
Journal for Geometry and Graphics
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Segeth, Karel
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Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the...
Jiří Kobza (1992)
Applications of Mathematics
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The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights and smoothing parameter , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter is mentioned.
Jiří Kobza, Radek Kučera (1993)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Zygmunt Wronicz (1985)
Annales Polonici Mathematici
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Vladimir Bogdanov, Wladimir Karsten, Valeriy Miroshnichenko, Yuriy Volkov (2013)
Open Mathematics
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A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from...
F.-J. Delvos, Walter Schempp (1972)
Mathematische Zeitschrift
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