Numerical Integration And Data Reduction For Application In Photometry - Chew, Tong Fatt (2003)
In this thesis, an algorithm based on a local interpolation scheme called the Average Angle Method was developed for numerical integration and data reduction of photometric data, and in general, for any data set sharing similar characteristics as the luminous intensity data The new interpolation scheme interpolates discrete data with piecewise cubic polynomials having a CI continuity in the interior. knots. The first derivatives at the interior knots are estimated from the average of the angles subtended to the horizontal by two adjacent slopes. In a further development, the algorithm is extended to create another algorithm using quintic polynomial interpolation that has C2 continuity, providing smoother interpolation curves but retaining the local nature of interpolation.