Geodesic
Cubic splines with minimal norm
Applications of Mathematics, Tome 47 (2002) no. 3, pp. 285-295
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Natural cubic interpolatory splines are known to have a minimal $L_2$-norm of its second derivative on the $C^2$ (or $W^2_2)$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^1$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.
Natural cubic interpolatory splines are known to have a minimal $L_2$-norm of its second derivative on the $C^2$ (or $W^2_2)$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^1$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.
DOI : 10.1023/A:1021749621862
Classification : 41A15, 65D05, 65D07
Keywords: cubic interpolatory spline; minimal norm interpolation 
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Kobza, Jiří. Cubic splines with minimal norm. Applications of Mathematics, Tome 47 (2002) no. 3, pp. 285-295. doi: 10.1023/A:1021749621862

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