CsAkima Class

Extension of the Spline class to handle the Akima cubic spline.

For a list of all members of this type, see CsAkima Members.

System.Object
Imsl.Math.Spline
Imsl.Math.CsAkima

public class CsAkima : Spline

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

Class CsAkima computes a cubic spline interpolant to a set of data points for $i = 0, \ldots, n-1$ . 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 $\xi$ be the breakpoint vector for the above spline interpolant. Then, the maximum absolute error satisfies

$\left\| {f - s} \right\|_{\left[ {\xi_0 , \xi_{n-1} } \right]} \le C\left\| f^{(2)}\right\|_{[\xi_0,\xi_{n-1}} \left| \xi \right|^2$

where

$|\xi| \;: = \max\limits_{i = 1,\ldots,n-1} |\xi_i -\xi_{i-1}|$

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.)

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

CsAkima Class

Thread Safety

Remarks

Requirements

See Also