Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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[SerializableAttribute] public class CsInterpolate : Spline |
Visual Basic (Declaration) |
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<SerializableAttribute> _ Public Class CsInterpolate _ Inherits Spline |
Visual C++ |
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[SerializableAttribute] public ref class CsInterpolate : public Spline |
Remarks
CsInterpolate computes a cubic spline interpolant to a set of data points for . The breakpoints of the spline are the abscissas. Endpoint conditions are automatically determined by the program. These conditions correspond to the "not-a-knot" condition (see de Boor 1978), which requires that the third derivative of the spline be continuous at the second and next-to-last breakpoint. If n is 2 or 3, then the linear or quadratic interpolating polynomial is computed, respectively.
If the data points arise from the values of a smooth, say, function f, i.e. , then the error will behave in a predictable fashion. Let be the breakpoint vector for the above spline interpolant. Then, the maximum absolute error satisfies
whereFor more details, see de Boor (1978, pages 55-56).