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Quadratic splines smoothing the first derivatives

Jiří Kobza (1992)

Applications of Mathematics

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 w i and smoothing parameter α , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter α is mentioned.

Quadrature formulas based on the scaling function

Václav Finěk (2005)

Applications of Mathematics

The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M 2 = M 1 2 and M 0 = 1 . So, in this sense, its choice is optimal. Numerical examples are given.

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