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Conference publicationsTwice continuously differentiable S-splinesRussia, Moscow In the article are presented the twice continuously differentiable S-splines, consisting from quintic polynomials. It is proved unique existence theorem and derived the condition of stability for such splines. First three coefficients of every polynomial of these splines are defined by “smooth glueing” conditions, but three rest coefficients are defined by the method of least squares. This provides their splines attribute to smooth source information. The particularity of these splines is its semi-locality i.e. each polynomial is implicitly defines on the value of functions, which participate for definition of the previous polynomials, and does not depend on values of functions defining the following polynomials. In this case the condition of stability is executed under hard limiting conditions (they can be enumerated in table). When the condition of stability is valid and the first polynomial of these splines approximates the given function, the spline approximates this function on all base interval. |
