This section is about numerical methods. Main goal of this work is to study (and improve if possible) classical methods of numerical analysis from the digital signal processing point of view. Specifically I’m interested in the improvement of noise robustness properties of the widely used algorithms.
This research led me to the conclusion that usual least-square approximation which is basement of many methods cannot guarantee noise robustness. I discovered new methods with guaranteed noise suppression for numerical differentiation, integration, interpolation, smoothing and missing data restoration.
So far I published results on Smooth noise-robust numerical differentiation. It has been used in several projects and received good response. There are distinct pages on Central differences, Savitzky-Golay (or Lanczos) filters where I study their properties and reasons why they don’t work well for noisy data.
I’m planning to add information on other algorithms in the nearest future – so don’t forget to bookmark my site and come here later.
Also I share source code and tables for the Gauss-Legendre quadrature of any order with high precision abscissas/weights.
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