High-Speed Scientific Computing Using Adaptive Spline Interpolation

The increasing scale of modern datasets has created a significant computational bottleneck for traditional scientific and statistical algorithms. To address this problem, the current paper describes and validates a high-performance method based on adaptive spline interpolation that can dramatically accelerate the calculation of foundational scientific and statistical functions. This is accomplished by constructing parsimonious spline models that approximate their target functions within a predefined, highly precise maximum error tolerance. The efficacy of the adaptive spline-based solutions was evaluated through benchmarking experiments that compared spline models against the widely used algorithms in the Python SciPy library for the normal, Student’s t, and chi-squared cumulative distribution functions. Across 30 trials of 10 million computations each, the adaptive spline models consistently achieved a maximum absolute error of no more than 1 × 10⁻⁸ while simultaneously ranging between 7.5 and 87.4 times faster than their corresponding SciPy algorithms. All of these improvements in speed were observed to be statistically significant at p < 0.001. The findings establish that adaptive spline interpolation can be both highly accurate and much faster than traditional scientific and statistical algorithms, thereby offering a practical pathway to accelerate both the analysis of large datasets and the progress of scientific inquiry.