CsInterpolate Class |
Namespace: Imsl.Math
The CsInterpolate type exposes the following members.
Name | Description | |
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CsInterpolate(Double, Double) |
Constructs a cubic spline that interpolates the given data points.
| |
CsInterpolate(Double, Double, CsInterpolateCondition, Double, CsInterpolateCondition, Double) |
Constructs a cubic spline that interpolates the given data points
with specified derivative endpoint conditions.
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Name | Description | |
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Derivative(Double) |
Returns the value of the first derivative of the spline at a point.
(Inherited from Spline.) | |
Derivative(Double, Int32) |
Returns the value of the derivative of the spline at a point.
(Inherited from Spline.) | |
Derivative(Double, Int32) |
Returns the value of the derivative of the spline at each point of an
array.
(Inherited from Spline.) | |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Eval(Double) |
Returns the value of the spline at a point.
(Inherited from Spline.) | |
Eval(Double) |
Returns the value of the spline at each point of an array.
(Inherited from Spline.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetBreakpoints |
Returns a copy of the breakpoints.
(Inherited from Spline.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
Integral |
Returns the value of an integral of the spline.
(Inherited from Spline.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
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).