Chapter 3 Interpolation and Approximation
Routines
Curve and Surface Fitting with Splines
Weighted least-squares fitting by B-splines to discrete
One-Dimensional data is performed
, SPLINE_FITTINGReturns a tensor product array result, given two arrays of
independent variable values
, SURFACE_VALUESWeighted least-squares fitting by tensor product B-splines
to discrete two-dimensional data is performed
, SURFACE_FITTINGCubic Spline Interpolation
Easy to use cubic spline routine
, CSIEZDerivative end conditions
, CSDECCubic Spline Evaluation and Integration
Evaluation of the derivative
, CSDEREvaluation on a grid
, CS1GDB-spline Interpolation
Easy to use spline routine
, SPLEZOne-dimensional interpolation
, BSINTKnot sequence given interpolation data
, BSNAKOptimal knot sequence given interpolation data
, BSOPKTwo-dimensional tensor product interpolation
, BS2INThree-dimensional tensor product interpolation
, BS3INSpline Evaluation, Integration, and Conversion to Piecewise Polynomial
Given the B-spline Representation
Evaluation of the derivative
, BSDEREvaluation on a grid
, BS1GDOne-dimensional integration
, BSITGTwo-dimensional evaluation
, BS2VLTwo-dimensional evaluation of the derivative
, BS2DRTwo-dimensional evaluation on a grid
, BS2GDTwo-dimensional integration
, BS2IGThree-dimensional evaluation
, BS3VLThree-dimensional evaluation of the derivative
, BS3DRThree-dimensional evaluation on a grid
, BS3GDThree-dimensional integration
, BS3IGConvert B-spline representation to piecewise polynomial
, BSCPPPiecewise Polynomial
Evaluation of the derivative
, PPDEREvaluation on a grid
, PP1GDQuadratic Polynomial Interpolation Routines for Gridded Data
One-dimensional evaluation
, QDVALOne-dimensional evaluation of the derivative
, QDDERTwo-dimensional evaluation
, QD2VLTwo-dimensional evaluation of the derivative
, QD2DRThree-dimensional evaluation
, QD3VLThree-dimensional evaluation of the derivative
, QD3DRMulti-dimensional Interpolation
Akima’s surface fitting method
, SURFMultidimensional interpolation and differentiation
, SURFNDLeast-Squares Approximation
General polynomial
, RCURVSplines with fixed knots
, BSLSQSplines with variable knot
, BSVLSSplines with linear constraints
, CONFTTwo-dimensional tensor-product splines with fixed knots
, BSLS2Three-dimensional tensor-product splines with fixed knots
, BSLS3Cubic Spline Smoothing
Smoothing by error detection
, CSSEDSmoothing spline using cross-validation
, CSSCVRational L∞Approximation
Rational Chebyshev
, RATCH