2020/01/24 by Haysn Hornbeck, Hornbeck, Haysn
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #Mathematical Software (cs.MS) #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2001.09253
openalex publication_date 2020/01/24 · openalex created_date 2020/01/30 · openalex updated_date 2026/07/28
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline interpolation, showing as much of our work as possible to allow for replication or criticsm. The output of the new algorithms is compared to the old, and found to be no different within the limits imposed by floating-point precision. Benchmarks of all these algorithms, plus variations which may run faster in certain instances, are performed. In general, all these algorithms have approximately the same execution time when interpolating curves with few control points on feature-rich Intel processors; as the number of control points increases or processor features are removed, the new algorithms become consistently faster than the old. Exceptions to that generalization are explored to create implementation guidelines, such as when to expect division to be faster than multiplication.