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java.lang.Object com.imsl.math.Spline com.imsl.math.CsAkima
Extension of the Spline class to handle the Akima cubic spline.
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.)
Field Summary |
Fields inherited from class com.imsl.math.Spline |
breakPoint, coef, EPSILON_LARGE |
Constructor Summary | |
CsAkima(double[] xData,
double[] yData)
Constructs the Akima cubic spline interpolant to the given data points. |
Methods inherited from class com.imsl.math.Spline |
copyAndSortData, copyAndSortData, derivative, derivative, derivative, getBreakpoints, integral, value, value |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
public CsAkima(double[] xData, double[] yData)
xData
- a double
array containing the x-coordinates of the data.
Values must be distinct.yData
- a double
array containing the y-coordinates of the data.
IllegalArgumentException
- This exception is thrown if
the arrays xData and yData do not have
the same length.
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