Schaums Functions

Like the o-Moms, the pseudo-Lagrangian kernels proposed by Schaum in [28] can also be represented as a weighted sum of B-splines and their even-order derivatives. They have same order and same support as B-splines and o-Moms. Their main

FIGURE 12 o-Moms of third degree (central part).

Function shape. (Right) Equivalent interpolant.

interest is that they are interpolants. Their main drawback with respect to both o-Moms and B-splines is a worse approximation constant C^: for the same approximation order L = 4, the minimal value is reached by o-Moms with Cv = 0.000627; the constant for the cubic spline is more than twice that, with Cv = 0.00166, while the cubic Schaum loses an additional order of magnitude with Cv = 0.01685. They have no regularity (are discontinuous) for even degrees, and are C0 for odd degrees. Figure 6 shows the quadratic member of that family.

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