CsAkima Class |
Namespace: Imsl.Math
The CsAkima type exposes the following members.
Name | Description | |
---|---|---|
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.) |
Class CsAkima 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; see Akima (1970) or de Boor (1978).
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
where
CsAkima is based on a method by Akima (1970) to combat wiggles in the interpolant. The method is nonlinear; and although the interpolant is a piecewise cubic, cubic polynomials are not reproduced. (However, linear polynomials are reproduced.)