That is, we offer a range of approaches by which a
tabulated function can be interpolated including cubic splines, polynomial
and rational interpolation for functions with 1 variable and bicubic splines
for functions of 2 variables.
Functionality Offered within this XML Web service
Within this XML Web service we consider the problem of approximating a function
of 1 or 2 real variables which is known on a discrete data set with a function which is
continuously differentiable in a neighborhood of all points at which it exists.
Below we list in sections corresponding to each of the generic types of interpolation
function the business methods which are contained within this XML Web service.
Cubic Interpolation of Variables (i.e. cubic splines)
CubicSpline2ndDifferential - Calculates the
second derivatives of the cubic spline interpolation polynomial at the tabulation points.
CubicSplinePointwisePreEvaluation - Evaluates
the cubic spline interpolation of a function at a point when the 2nd differentials at the
tabulation points are known.
CubicSplinePointwise - Calculates the value of the
cubic spline interpolation when the end point derivatives are known.
CoefficientsInterpolatingPolynomialStable
- A stable (and slower) means by which to evaluate the coefficients of the interpolating polynomial of
1 variable when the tabulation points are known.
CoefficientsInterpolatingPolynomial
- A fast (and less stable) means by which to evaluate the coefficients of the interpolating polynomial of
1 variable when the tabulation points are known.
Rational Function Interpolation of one variable
RationalInterpolationExtrapolation - Evaluates
the value and the corresponding error estimate at a given point of the rational interpolation
function.
Evaluation of the Bicubic interpolation function of two variables
BicubicCoefficients - Calculates
the coefficients for the bicubic interpolation polynomial.
BicubicInterpolation(double[], ...)
- Evaluates the value of the bicubic interpolation polynomial at a point and the derivatives in the directions
of the grid.
BicubicInterpolation(double[][], ...)
- Evaluates the values of the bicubic interpolation polynomial at a point and the derivatives in the directions
of the grid when its coefficients are known.