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Cubic Splines as a Special Case of Restricted Least Squares
Journal of the American Statistical Association, 1977Abstract The standard cubic spline regression method is shown to be a special case of the restricted least-squares estimator. The equivalence of the two procedures under a common set of restrictions is proved. The greater flexibility of the restricted least-squares estimator in terms of the number of restrictions and tests of hypotheses that can be ...
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A second-order method based on quartic non-polynomial spline consisting of a polynomial part of degree two and a trigonometric part is developed to find continuous approximation of a two point boundary-value problem involving a third-order differential equation. It is shown that the angular frequency k of the trigonometric part can be used to raise the
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Positive-definite splines of special form
Sbornik: Mathematics, 2002Even positive-definite splines with support in \([ - 1,1]\) that are equal to a real algebraic polynomial on \([0,1]\) are investigated. Examples of such splines are presented. Under consideration are \(e\)-splines, which have several extremal properties, and the positive definite \(A\)-splines, which have the maximum possible smoothness on \(R\).
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The Beta2-spline: A Special Case of the Beta-spline Curve and Surface Representation
IEEE Computer Graphics and Applications, 1985Simpler equations and computationally more efficient algorithms make the Beta2-spline technique easier to understand and useful to the designer.
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