Cubic spline algorithm

Data points XJ3 Yj) were curve-fitted using a precise continuous polynomial, or cubic spline, algorithm. Ordinate values were represented as... 

Neuman, C. P., and Sen, A., A suboptimal control algorithm for constrained problems using cubic splines, Automatica 9, 601-613 (1973). 

Numerical methods for interpolating between data points or over data point intervals are often better, since no a priori assumptions are made. There is a very wide variety of interpolation methods available, such as cubic splines, which guarantee continuity and differentiability of the interpolated data. Some programs, such as Mathematica , have a wide variety of such menus built into their powerful data handling and representation algorithms. 

The sky frames were combined with a median filter percentile-dipping algorithm and used for flat fielding. This technique eliminates stars in the sky frames to 0.1%, comparable with the residual spatial noise in the source frames. Dark current was not subtracted as it is negligible (< 1 e s ). The flat-fielded source frames were combined by first determining the spatial offsets, thm rebinning with a cubic spline to a common refermce, and finally combining with a median filter. The residual spatial noise is 0.1% or bettor. 

How are the Bj k(t) functions computed An efficient way is to use the Cox-DeBoor algorithm [18,19] which is based on a recursive formulation of the Bj,k(t) functions. Using a cubic B-spline to illustrate, it is possible to write out the recursive steps explicitly ... 

---