Displaying similar documents to “On the application of the orthonormal Franklin system to the approximation of analytic functions”

Cubic splines with minimal norm

Jiří Kobza (2002)

Applications of Mathematics

Similarity:

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...

Natural and smoothing quadratic spline. (An elementary approach)

Jiří Kobza, Dušan Zápalka (1991)

Applications of Mathematics

Similarity:

For quadratic spine interpolating local integrals (mean-values) on a given mesh the conditions of existence and uniqueness, construction under various boundary conditions and other properties are studied. The extremal property of such's spline allows us to present an elementary construction and an algorithm for computing needed parameters of such quadratic spline smoothing given mean-values. Examples are given illustrating the results.