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 results of a 1D numerical example that show the advantages and drawbacks of the tension spline.

EUDML-ID : urn:eudml:doc:287813
Mots clés:
Mots clés:

@article{702978,
     title = {A note on tension spline},
     booktitle = {Application of Mathematics 2015},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics CAS},
     address = {Prague},
     year = {2015},
     pages = {217-224},
     zbl = {06669932},
     url = {http://dml.mathdoc.fr/item/702978}
}

Segeth, Karel. A note on tension spline, dans Application of Mathematics 2015, GDML_Books,  (2015), pp. 217-224. http://gdmltest.u-ga.fr/item/702978/